System and Method for Monitoring and Controlling Underground Drilling

ABSTRACT

A system and method for monitoring underground drilling in which vibration is monitored by creating a model of the drill string using finite element techniques or finite difference techniques and (i) predicting vibration by inputting real time values of operating parameters into the model, and then adjusting the model to agree with measured vibration data, (ii) predicting the weight on bit and drill string and mud motor speeds at which resonance will occur, as well as when stick-slip will occur, so that the operator can avoid operating regimes that will result in high vibration, (iii) determining vibration and torque levels along the length of the drill string based on the measured vibration and torque at one or more locations, (iv) determining the remaining life of critical components of the drill string based on the history of the vibration to which the components have been subjected, and (v) determining the optimum drilling parameters that will avoid excessive vibration of the drill string.

FIELD OF THE INVENTION

The present invention relates to underground drilling, and morespecifically to a system and a method for monitoring and controlling thedrilling operation, especially operation related to drill stringvibration, so as to achieve optimum performance and life from the drillstring.

BACKGROUND OF THE INVENTION AND RELATED ART

Underground drilling, such as gas, oil, or geothermal drilling,generally involves drilling a bore through a formation deep in theearth. Such bores are formed by connecting a drill bit to long sectionsof pipe, referred to as a “drill pipe,” so as to form an assemblycommonly referred to as a “drill string.” The drill string extends fromthe surface to the bottom of the bore.

The drill bit is rotated so that the drill bit advances into the earththereby forming the bore. In rotary drilling, the drill bit is rotatedby rotating the drill string at the surface. Piston-operated pumps onthe surface pump high-pressure fluid, referred to as “drilling mud,”through an internal passage in the drill string and out through thedrill bit. The drilling mud lubricates the drill bit, and flushescuttings from the path of the drill bit. In the case of motor drilling,the flowing mud also powers a drilling motor, commonly referred to as a“mud motor,” which turns the bit, whether or not the drill string isrotating. The mud motor is equipped with a rotor that generates a torquein response to the passage of the drilling mud therethrough. The rotoris coupled to the drill bit so that the torque is transferred to thedrill bit, causing the drill bit to rotate. The drilling mud then flowsto the surface through an annular passage formed between the drillstring and the surface of the bore.

The drilling environment, and especially hard rock drilling, can inducesubstantial vibration and shock into the drill string. Vibration alsocan be introduced by rotation of the drill bit, the motors used torotate the drill bit, the pumping of drilling mud, imbalance in thedrill string, etc. Such vibration can result in premature failure of thevarious components of the drill string, premature dulling of the drillbit, or may cause the drilling to be performed at less than optimumconditions. For example, although reducing the downhole force applied tothe drill bit, commonly referred to as the “weight on bit” (“WOB”) orthe rotary speed of the drill bit may reduce vibration, it may alsoreduce drilling efficiency. In particular, drill bits are typicallydesigned for a predetermined range of rotary speed and WOB and do notperform as effectively if operated outside this range in order to avoidexcessive vibration. Moreover, operating the drill bit away from itsdesign point can reduce the service life of the drill bit. Substantialvibration can even directly reduce the rate of penetration of the drillbit. For example, very high axial vibration can result in a loss ofcontact between the drill bit and the surface being drilled.

A drill string may experience various types of vibration. “Axialvibration” refers to vibration in the direction along the drill stringaxis. “Lateral vibration” refers to vibration perpendicular to the drillstring axis. Lateral vibration often arises because the drill stringrotates in a bent condition. Two other sources of lateral vibration are“forward” and “backward”, or “reverse”, whirl. “Whirl” refers to asituation in which the bit orbits around the bore hole in addition torotating about its own axis. In backward whirl, the bit orbits in adirection opposite to the direction of rotation of the drill bit.“Torsional vibration,” also of concern in underground drilling, isusually the result of what is referred to as “stick-slip.” Stick-slipoccurs when the drill bit or lower section of the drill stringmomentarily stops rotating (i.e., “sticks”) while the drill string abovecontinues to rotate, thereby causing the drill string to “wind up,”after which the stuck element “slips” and rotates again. Often, the bitwill over-speed as it unwinds.

In general, optimal drilling is obtained when the rate of penetration ofthe drill bit into the formation is as high as possible while thevibration is as low as possible. The rate of penetration (“ROP”) is afunction of a number of variables, including the rotational speed of thedrill bit and the WOB. During drilling, surface equipment senses therate of penetration of the drill bit into the formation, the rotationalspeed of the drill string, the hook load, surface torque, and pressure.Sensors either at the surface or in a bottomhole assembly (“BHA”), orboth, measure the axial tensile/compression load, torque and bending.

APS's SureShot™ Surface System

Systems currently on the market, such as APS Technology's SureShot™surface system, receive and process information from sensors near thebit, such as WOB sensors, torque sensors, inclination sensors (i.e.,accelerometers) and azimuth sensors (i.e., magnetometers), and transmitthe information to other surface equipment. A surface estimate of WOBmay also be derived from hook load and drag calculations. The SureShot™system also receives data on the mud flow rate from other surfacesoftware. Typically, such software determines the mud flow rate from acurve provided by the mud pump supplier relating flow rate to strokerate of the pump pistons, rather than from a direct flow rate sensors.In any event, using a curve of mud motor flow rate versus motor RPM oran RPM/flow rate factor, the surface software also determines the mudmotor RPM. The SureShot™ system also calculates the build rate, normallyexpressed as degrees per 100 feet or degrees per 30 meters, based on thechange in inclination measured by the accelerometers for the depthdrilled. It also calculates the turn rate, normally expressed as degreesper 100 feet or degrees per 30 meters, based on the change in azimuth(i.e., the lateral direction of drilling) measured by the magnetometers.However, notwithstanding the availability of such data, obtaining theoptimal rate of penetration is a difficult endeavor. Optimization of thedrilling process is a constantly changing and ongoing process.Formations may change, bits may dull, mud weight and the hydraulics maychange.

APS's Vibration Memory Module™

Systems currently on the market, such as APS Technology's VibrationMemory Module™, process data from accelerometers and magnetometersinstalled into the bottomhole assembly to determine the amplitudes ofaxial vibration, and of lateral vibration due to forward and backwardwhirl, at the location of these sensors. The Vibration Memory Module™also determines torsional vibration due to stick-slip by measuring andrecording the maximum and minimum instantaneous RPM over a given periodof time, such as every four seconds, based on the output of themagnetometers. The amplitude of torsional vibration due to stick-slip isthen determined by determining the difference between and maximum andminimum instantaneous rotary speeds of the drill string over the givenperiod of time. Preferably, root-mean-square and peak values for theaxial, lateral and torsional vibrations are recorded at predeterminedintervals, such as every four seconds. The amplitudes of the axial,lateral and torsional vibration are transmitted to the surface via mudpulse telemetry.

Most systems, including the aforementioned Vibration Memory Module™,don't measure the frequency of the vibration, although some high endtools do. Insofar as the inventors are aware, none of the current tools,however, transmit the vibration frequency to the surface. However, whenusing the Vibration Memory Module™, burst data samples, recorded eitheras a result of the occurance of an event or at preselected time periods,may be down loaded from the Vibration Memory Module™ after a run iscompleted and the BHA assembly is pulled out of the hole. Software atthe surface can read the burst sample data, plot it and performs aFourier analysis to determine the frequency of the vibration.

APS's Well Drill™

Other systems on the market, such as APS Technology's Welldrill™ systememploy finite element techniques to predict the resonant frequencies andmode shapes associated with drill string vibration. The WellDrill™system employs software that uses finite element techniques, inparticular ANSYS software, to model the drill string based on the drillstring geometry and mechanical properties. As shown in FIG. 1, the modelis comprised of beam elements 2, connected by nodes 3, and contactelements 5. As shown in FIG. 2, the entire drill string 4—including adrill bit 8, mud motor 40, stabilizers 41, drill collars 43, MeasurementWhile Drilling (“MWD”) tool 45—is modeled by a series of beam elements,nodes and contact elements. A beam element 2 is shown in FIG. 3A andcomprises a uniaxial element with tension, compression, torsion, andbending capabilities. These elements have six degrees of freedom at eachnode: translations in the nodal x, y and z directions and rotationsabout the nodal x, y and z axes. Stress stiffening and large deflectioncapabilities are also included. The gaps between drill string componentsand the borehole are modeled using contact elements, each of whichrepresents two surfaces which may maintain or break physical contact andmay slide relative to each other. A contact element 5, shown in FIG. 3B,is capable of supporting only compression in the direction normal to thesurfaces and shear (Coulomb) friction in the tangential direction, andhave two degrees of freedom at each node: translations in the nodal xand y directions. Force and displacement constraints are applied to anode at each end of a drill string element and a contact element isattached to each node. The drill string is allowed to deflect laterally,until it contacts the surface modeled by the contact element.

In particular, the WellDrill™ model of the drill string is created byentering data into the software to specify:

-   -   (i) the outside and inside diameters of the drill pipe sections        that make up the drill string,    -   (ii) the locations of stabilizers,    -   (iii) the length of the drill string,    -   (iv) the inclination of the drill string,    -   (v) the bend angle if a bent sub is used,    -   (vi) the material properties, specifically the modulus of        elasticity, material density, torsional modulus of elasticity,        and Poisson's ratio,    -   (vii) the mud properties for vibration damping, specifically,        the mud weight and viscosity,    -   (viii) the bore hole diameters along the length of the well        obtained by adding an increment (e.g., 0.25 inch (6.4 mm)) to        the diameter of the drill bit based on the type of formation,    -   (ix) the azimuth, build rate and turn rate,    -   (x) the diameter of the drill bit and stabilizers, and    -   (xi) information concerning the characteristics of the        formation, such as the strike and dip. These are used when the        formation is a non-homogenous material, having different        compressive strengths in orthogonal directions.

Strike is defined as the compass direction, relative to north, of theline formed by the intersection of a rock layer or other planar featurewith an imaginary horizontal plane. The intersection of two flat planesis a straight line, and in this instance, the line is geologic strike.According to convention, the compass direction (or bearing) of this lineis always measured and referred to relative to north. A typical bearingis given, for example, as N 45° E, which is a shorthand notation for abearing that is 45° east of north (or half way between due north and dueeast). The only exception to this north rule occurs where strike isexactly east-west. Then, and only then, is a strike direction writtenthat is not relative to north. Dip, as a part of the measurement of theattitude of a layer or planar feature, has two components: dip directionand dip magnitude. Dip direction is the compass direction (bearing) ofmaximum inclination of the layer or planar feature down from thehorizontal and is always perpendicular (i.e., at a 90° angle) to strike.Dip magnitude is the smaller of the two angles formed by theintersection of the dipping layer or planar feature and the imaginaryhorizontal plane. However, dip magnitude can also be equal to eitherzero or 90°, where the layer or planar feature is horizontal orvertical, respectively.

From the data inputs specified above, the WellDrill™ software calculatesthe static deflection shape of the drill string so as to determine thepoints of contact between the drill string and the bore hole.

In addition, data are also entered into the WellDrill™ softwarespecifying the expected operating parameters for (i) the WOB, (ii) thedrill string RPM, (iii) the mud motor RPM, (iv) the diameter of the borehole, and (v) the damping coefficient. The damping coefficient iscalculated using a predetermined values of the viscosity of oil or water(depending on whether the operator indicates that an oil-based orwater-based drilling mud is used), the density of the fluid (mudweight), and the annulus between the BHA and the bore hole. The borehole diameter is estimated based on the diameter of the drill bit andthe type of formation in lieu of not having caliper data. For example,if the formation is hard rock, the diameter of the bore hole may beestimated to be ½ inch larger than the diameter of the drill bit,whereas it may be estimated to be much larger than the drill bit forsoft rock. (The maximum diameter is based on the number of cones orblades on the bit.) The diameter of the bore hole is also generallyassumed to be bigger if a bent sub is used for rotary directionaldrilling.

As noted above, the WellDrill™ software performs static bending analysisto determine contact points between the drill string and the borehole.This provides support information for the vibration analysis. The staticbending analysis determines the deflection, contact points, bendingmoments and the bending stress along the length of the drill string. Thebending analysis is used to determine the predicted build and turn rate.The build rates are determined by a force balance at the drill bit. Thecritical speeds are determined by performing a forced harmonic frequencysweep. Excitation forces are applied at the bit and the power section ofthe mud motor. Wherever the excitation forces are near naturalfrequencies of the drill string, critical speeds occur.

In particular, the WellDrill™ software performs a forced responseanalysis by applying an oscillating WOB over selected range of WOBs anddrill bit RPMs. The selected oscillating WOB is applied at twofrequencies: (i) the rotary speed of the drill bit and (ii) the numberof cones (for roller cone bits) or blades (for PDC bits) multiplied bythe drill bit speed. Since mud motors rotors are eccentric by design,they always create an oscillating imbalance force, the magnitude ofwhich is based on the rotor eccentricity and the frequency of which isequal to N(n+1), where n is the number of lobes on the rotor and N isthe mud motor rotor RPM. Therefore, if a mud motor is used, the softwareincludes in the forced response analysis an oscillating imbalance forcebased on the characteristics of the mud motor applied at frequenciesbased on a selected range of mud motor RPM. Typical drill string rotaryspeeds are 10-250 rpm, while mud motor speeds may be 50-250 rpm. Thetypical bit speed (combination of motor and rotary speeds) is,therefore, 60 to 500 rpm. Mud turbines operate at much higher speeds of800-1500 rpm, but do not introduce a similar imbalance. Drill collarsmay also have features, such as electronics hatches, upsets and cutout,that create a rotating imbalance. In addition, drill collars that becomebent in service create a rotating imbalance. Since such rotatingimbalances are a source of vibration excitation, WellDrill™ can includethem in the model.

Based on the foregoing, the WellDrill™ software predicts criticaldrilling speeds for the drill string, motor and bit. Critical speedsoccur when the drilling forces excite the drill string such that theinduced vibration causes damage to the drill string and/or results inlost drilling performance. Drilling forces that may excite the drillingand induce critical speeds include: bit forces from the blades or conesof the bit striking a discontinuity, bit whirling in an over gauge borehole, the imbalance forces generated by the motor stator, imbalanceforces from the drill string the drill string contacting the bore holeresulting in whirling, and under-gauge stabilizers whirling. Typically,when the frequency of the excitation force is at or near a naturalfrequency of the drill string, the displacement amplitudes are easier toexcite. In addition, in severe drilling applications the excitationforces away from the natural frequencies may be severe enough to damagethe drillstring and require their identification as critical speeds.

The WellDrill™ software also calculates the torque at each section alongthe drill string using the equation:

T=θ J G/L

Where: T=torque

-   -   θ=angular displacement    -   J=polar moment of inertia    -   G=shear modulus    -   L=length of the drill string section

WellDrill™ uses the calculated torque to determine torsional vibrationsby determining whether the torque applied to the drill bit is sufficientto rotate the drill string backward. If this condition is present thenit is considered a torsional critical speed. WellDrill™ also uses thecalculated torque to determine stick-slip conditions, in particular,whether the torque along the drill string is sufficient to overcomefrictional resistance to rotation.

Stick-Slip Software

Software has also been used in the past to predict when stick-slip willoccur using a finite difference technique. First, the softwarecalculates the drag along the entire length of the drill string and atthe bit. The calculation of drag is based on the methodology describedin C. A. Johancsik et al., Torque And Drag In DirectionalWells—Prediction and Measurement, Journal of Petroleum Technology,987-992 (June 1984), herein incorporated by reference in its entirety.

The previously used stick-slip prediction software breaks up the drillstring into finite lengths, typically less than thirty feet. The drag oneach section is a function of the normal force the section exerts on thewall of the borehole and the coefficient of sliding friction between thedrill string and the wall. The normal force is a function of thecurvature of the drill string section, the tension in the section, andgravity effects. The coefficient of friction is primarily a function ofthe characteristics of the drilling mud and whether the borehole iscased or open. Its value can be empirically developed by, for example,applying the model to a drill string in which the pickup weight,slack-off weight and torque are measured to establish independentmeasurements of drag.

The software calculates the drag on each section of drill string as theincremental moment, ΔM, necessary to overcome the friction force, fromthe equations:

ΔF _(n)=[(F _(t)Δα sin θ_(A))²+((F _(t) Δθ+W sin θ_(A))²]^(1/2)

-   -   ΔF_(t)=W cos θ_(A)±[+for upward motion, −for downward motion]    -   ΔM=μ F_(n) r    -   Where:        -   F_(n)=net normal force acting on the section, lb-ft (N-m)        -   F_(t)=axial tenstion acting at the lower end of the length            of section, lb-ft (N-m)        -   ΔF_(t)=increase in tension over the length of section, ft-lb            (N-m)        -   ΔM=increase in torsion over the length of section, ft-lb            (N-m)        -   r=characteristic radius of the section, ft (m)        -   W=buoyed weight of the section, lb (N)        -   Δα=increase in azimuth angle over length of the section,            degrees (rad)        -   Δθ=increase in inclination angle over length of section,            degrees (rad)        -   θ_(A)=average inclination angle of section, degrees (rad)        -   μ=sliding coefficient of friction between drill string and            borehole

The calculations start at the surface with an initial rotary speed of 0rpm. The software uses the static friction coefficient when the pipe isstationary, and the sliding friction coefficient when it is movingrelative to the borehole (sliding and/or rotating.). Normally the staticfriction is higher than the sliding friction. Next, the softwarecalculates the torsional deflection in each section as a result of theincremental torque, ΔM, based on the mechanical properties of thesection. The section properties depend on the outside and insidediameters of the section and its material density. These define the massof the section and the rotational inertia of each section. If the sum ofthe incremental torques necessary to overcome the drag is greater thanthe torque applied to the drill string, at the surface, then the drillbit will “stick.” The software then determines what values of WOB anddrill string RPM, will result in stick-slip.

In addition, the software calculates the rotary inertia—that is, theincremental time it will take each section to deflect by that amountbased on the mechanical properties of the section, in particular, theinside and outside diameter of the section and its mass, the appliedtorque and friction. The sum of these time increments over the length ofthe drill string represents the change in the instantaneous speed of thedrill string, which is reported to operating personal for use, forexample, in operating a rotary steerable tool or ensuring that theoperating conditions are not damaging the drill bit.

While such predictions of resonant frequencies, mode shapes and stickslip provided in the past, as discussed above, can aid the operator inidentifying those values of the drilling parameters, such as drillstring RPM and WOB, to be avoided in order to avoid excessive vibration,they do not make use of real-time data as the drilling progresses noradequately account for changes in drilling conditions over time. Neitherdo they provide methods for mitigating poor drilling performance,especially vibration-related losses in drilling performance, or foroptimizing drilling efficiency, or for determining the remaining fatiguelife of critical components. Their usefulness is, therefore, limited.

An ongoing need therefore exists for a system and method for providingthe drill rig operator with accurate information concerning vibrationbased on actual operating data that will allow optimum performance andtool life.

SUMMARY OF THE INVENTION

In one embodiment, the invention encompasses a method, which may becomputer implemented, of monitoring the operation of a drill stringdrilling into an earthen formation so as to form a bore hole using adrill bit, comprising the steps of: (a) drilling a bore hole having afirst diameter in the earthen formation by rotating the drill bit at afirst rotary speed and applying a first weight on the bit; (b) making adetermination of the value of the first rotary speed at which the drillbit rotates; (c) making a determination of the value of the first weighton the bit; (d) making a determination of the value of the firstdiameter of the bore hole; (d) measuring vibration in the drill stringat least one predetermined location along said drill string whilerotating said drill bit at said first speed and applying the firstweight on the bit; (e) using a finite element model of the drill stringto predict the vibration in the drill string at the at least onepredetermined location based on the determined values of the firstrotary speed of the drill bit, the first weight on bit and the firstbore hole diameter; (f) comparing the measured vibration to thepredicted vibration and determining the difference therebetween; (g)revising the finite element model so as to reduce the difference betweenthe measured vibration and the vibration predicted by the model; (h)drilling a bore hole having a second diameter in said earthen formationby rotating said drill bit at a second rotary speed and applying asecond weight on said bit; (i) making a determination of the value ofthe second rotary speed at which said drill bit rotates; (j) making adetermination of the value of said second weight on said bit; (k) makinga determination of the value of said second diameter of the bore hole;(l) using the revised finite element model of the drill string topredict the vibration in the drill string based on the determined valuesof the second rotary speed of the drill bit, the second weight on bitand the second bore hole diameter.

In another embodiment, the invention encompasses a method, which may becomputer implemented, for monitoring the operation of a drill stringdrilling into an earthen formation so as to form a bore hole using adrill bit located in a bottom hole assembly, comprising the steps of: a)determining the values of a plurality of operating parameters associatedwith the underground drilling operation by taking measurements from aplurality of sensors, at least a portion of the sensors located in thebottom hole assembly; b) determining from the determined values of theoperating parameters whether each of a plurality of predeterminedsymptoms of lost drilling performance are present in the drillingoperation; c) identifying the probability that each of the parametersdetermined to be present in the drilling operation are caused by each ofa plurality of predetermined causes of lost drilling performance; d)combining the identified probabilities for each of the predeterminedcauses of lost drilling performance so as to determine the most likelycause of lost drilling performance present in the drilling operation.

In another embodiment, the invention encompasses a method, which may becomputer implemented, for monitoring the operation of a drill stringdrilling into an earthen formation so as to form a bore hole using adrill bit, comprising the steps of a) operating the drill string at afirst set of operating parameters, the first set of operating parameterscomprising the speed at which the drill bit rotates; b) determining thevalues of the parameters in the first set of operating parameters; c)inputting the determined values of the parameters in the first set ofoperating parameters into a finite element model of the drill string; d)using the finite element model of the drill string with the inputtedvalues of the parameters to determine at least a portion of thevibratory mode shape of the drill string when operating at the first setof operating parameters; e) using the portion of the vibratory modeshape to determine the relationship between the amplitude of vibrationat the first location to the amplitude of vibration at a second locationwhen operating at the first set of operating parameters; f) measuringthe amplitude of vibration of the drill string at the second locationwhen operating at the first set of operating parameters; g) determiningthe amplitude of vibration of the drill string at the first location byapplying to the measured vibration at the second location therelationship between the amplitude of vibration at the first location tothe amplitude of vibration at a second location determined from theportion of the vibratory mode shape.

In another embodiment, the invention encompasses a method, which may becomputer implemented, for monitoring the operation of a drill stringdrilling into an earthen formation so as to form a bore hole using adrill bit, comprising the steps of: a) applying a torque to the drillstring at a location proximate the surface of the earth so as to rotatethe drill string, the drill string undergoing angular deflection betweenthe drill bit and the location at which the torque is applied; b)determining the values of parameters in a first set of operatingparameters associated with the rotation of the drill string; c)inputting the determined values of the parameters in the first set ofoperating parameters into a finite element model of the drill string; d)using the finite element model of the drill string with the inputtedvalues of the parameters to determine the angular deflection in thedrill string at at least first and second locations along the length ofthe drill string when operating at the first set of operatingparameters; e) using the angular deflections at the first and secondlocations along the drill string to determine the relationship betweenthe torque on the drill string at the first and second locations; f)measuring the torque on the drill string at the second location whenoperating at the first set of operating parameters; g) determining thetorque on the drill string at the first location by applying to themeasured torque at the second location the relationship between thetorque on the drill string at the first location to the torque on thedrill string at the second location.

In another embodiment, the invention encompasses a method, which may becomputer implemented, for monitoring the operation of a drill stringdrilling into an earthen formation so as to form a bore hole using adrill bit, comprising the steps of: a) rotating the drill bit at a firstrotary speed so that the drill bit forms a bore hole in the earthenformation, the drill string vibrating in a lateral vibration mode; b)generating a signal representative of the vibration of the drill stringin the lateral vibration mode as the drill bit drills into the earthenformation; c) analyzing the signal so as to determine the backward whirlfrequency of the vibration of the drill string in the lateral vibrationmode; d) determining the diameter of the bore hole being drilled by thedrill bit from the backward whirl frequency.

In another embodiment, the invention encompasses a method, which may becomputer implemented, for monitoring the operation of a drill stringdrilling into an earthen formation so as to form a bore hole using adrill bit, comprising the steps of: a) determining a set of operatingparameters for the drill string that will result in the maximum rate ofpenetration of the drill bit into the earthen formation; b) inputtingthe set of operating parameters into a finite element model of the drillstring; and c) using the finite element model with the inputted set ofoperating parameters to predict the vibration in the drill string thatwill result from operation of the drill string according to the set ofoperating parameters.

In another embodiment, the invention encompasses a method, which may becomputer implemented, for monitoring the operation of a drill stringdrilling into an earthen formation so as to form a bore hole using adrill bit, comprising the steps of: a) obtaining a data base relatingsets of operating parameters for the drill string to rates ofpenetration of the drill bit into the earthen formation when operatingat the sets of operating parameters; b) using a finite element model ofthe drill string and the data base to predict the maximum rate ofpenetration of the drill string into the earthen formation that will notresult in the vibration in the drill string violating a predeterminedcriteria.

In another embodiment, the invention encompasses a computer-readablestorage medium having stored thereon computer-exectuable instructionsfor performing the aforementioned methods.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing summary, as well as the following detailed description ofa preferred embodiment, are better understood when read in conjunctionwith the appended diagrammatic drawings. For the purpose of illustratingthe invention, the drawings show embodiments that are presentlypreferred. The invention is not limited, however, to the specificinstrumentalities disclosed in the drawings.

FIG. 1 is a schematic diagram of a finite element model used to model adrill string.

FIG. 2 is a schematic diagram of a finite element model of a drillstring.

FIGS. 3A and B are schematic diagrams of beam and contact elements usedin the finite element model of the drill string.

FIG. 4 is a view, partly schematic, of a drilling rig incorporating thecurrent invention.

FIG. 5A is a flowchart of the method of operating a drill string that isthe subject of the current invention.

FIG. 5B is a flowchart of the method of creating a model of the drillstring using the WellDrill™ software.

FIG. 6 is a flowchart of a method for revising the drill string model toreduce deviations between predicted and measured critical speeds.

FIG. 7 is a hypothetical vibratory mode shape curve generated using thesoftware of the current invention.

FIG. 8 is a hypothetical critical speed map created by the software ofthe current invention.

FIG. 9 is a flowchart of the method of identifying the cause of loss ofdrilling performance according to the current invention.

FIGS. 10-12 are flowcharts of the method of mitigating lost performancein drill performance, due to vibration, according to the currentinvention.

FIG. 13 is a flowchart of the method for revising the drill string modelto reduce deviations between predicted and measured vibration, followingmitigation of lost drilling performance due to vibration, according tothe current invention.

FIG. 14 is a flowchart of the method for revising the model to reducedeviations between predicted and measured vibration when mitigation of aloss of drilling performance due to vibration has not been attempted,according to the current invention.

FIG. 15 is a flowchart of the method for operating at the maximum rateof penetration that avoids excessive vibration.

DESCRIPTION OF PREFERRED EMBODIMENTS

As shown in FIG. 4, drill rigs typically comprise a derrick 9 thatsupports a drill string 4. A drill bit 8 is coupled to the distal end ofa bottomhole assembly 6 of the drill string 4. A prime mover (notshown), such as a top drive or rotary table, rotates the drill string 4so as to control the rotational speed (RPM) of, and torque on, the drillbit 8. As is conventional, a pump 10 pumps a fluid 14—typically referredto as drilling mud—downward through an internal passage in the drillstring. After exiting at the drill bit 8, the returning drilling mud 16flows upward to the surface through an annular passage formed betweenthe drill string 4 and the bore hole 2 in the earthen formation 3. A mudmotor 40, such as a helicoidal positive-displacement pump—sometimesreferred to as a “Moineau-type” pump—may be incorporated into thebottomhole assembly 6 and is driven by the flow of drilling mud 14through the pump. A helicoidal positive-displacement pump is describedmore fully in U.S. Pat. No. 6,102,681, entitled “Stator EspeciallyAdapted For Use In A Helicoidal Pump/Motor,” hereby incorporated byreference herein in its entirety.

A. Instrumentation and Hardware 1. Downhole Instrumentation

According to the current invention, preferably, downhole strain gauges 7are incorporated into the bottomhole assembly 6 to measure the WOB. Asystem for measuring WOB using downhole strain gauges is described inU.S. Pat. No. 6,547,016, entitled “Apparatus For Measuring Weight AndTorque An A Drill Bit Operating In A Well,” hereby incorporated byreference herein in its entirety. In addition to downhole sensorsmeasuring the WOB, downhole sensors, such as strain gauges, measuringthe torque on bit (“TOB”) and the bending on bit (“BOB”) are alsoincluded in the bottomhole assembly. Techniques for downhole measurementof TOB are also described in the aforementioned U.S. Pat. No. 6,547,016,incorporated by reference above. Techniques for the downhole measurementof BOB are described in U.S. application Ser. No. 12/512,740, filed Jul.30, 2009, entitled “Apparatus for Measuring Bending on a Drill BitOperating in a Well,” hereby incorporated by reference in its entirety.A sub incorporating WOB, TOB and BOB sensors is referred to as a “WTBsub.”

A magnetometer 42 is incorporated into the bottomhole assembly 6 thatmeasures the instantaneous rotational speed of the drill bit 8, using,for example, the techniques in U.S. Patent Application Publication No.2006/0260843, filed May 1, 2006, entitled “Methods And Systems ForDetermining Angular Orientation Of A Drill String,” hereby incorporatedby reference herein in its entirety. Accelerometers 44, oriented alongthe x, y. and z axes (typically with ±250 g range), are incorporatedinto the bottomhole assembly 6 that, using techniques well known in theart, measure axial and lateral vibration. Although accelerometers 44 areshown in only one location in FIG. 4, as is conventional, sets of threex, y, z accelerometers would be installed at various locations along thedrill string 4.

A Vibration Memory Module™ 46, discussed above, is preferablyincorporated into the bottomhole assembly 6. It receives data from theaccelerometers 44 installed into the bottomhole assembly 6, from whichit determines the amplitude and frequency of axial vibration, and oflateral vibration due to forward and backward whirl, at the location ofthe accelerometers. These values are transmitted to the surface via amud pulse telemetry system, discussed below. Alternatively, theinformation could be transmitted to the surface using a wired pipesystem, such as Intellipipe, or other means such as acoustic orelectromagnetic transmission. The Vibration Memory Module™ 46 alsoreceives data from the magnetometer 42 incorporated into the bottomholeassembly 6, from which it measures the instantaneous rotational speed ofthe drill string at the magnetometer 42 location. It then determines theamplitude and frequency of torsional vibration due to stick-slip bydetermining the difference between and maximum and minimum instantaneousrotational speed of the drill string over a given period of time. Thisinformation is also transmitted to the surface via the mud pulsetelemetry system. According to the current invention, a memory device47, such as a micro-chip, is incorporated into the Vibration MemoryModule™ 46 to record the fatigue life remaining in the component, asdiscussed in section 10, below, concerning life prediction. In addition,pressure sensors 51 and 52 are incorporated into the Vibration MemoryModule™ 46 that measure the pressure of the drilling mud flowing throughthe drill string and the pressure of the drilling mud flowing throughthe annular gap between the bore hole wall and the drill string,respectively.

2. Surface Instrumentation

As is conventional, the WOB is controlled by varying the hook load onthe derrick 9. A top sub 45 is incorporated at the top of the drillstring and encloses strain gauges 48 that measure the axial (hook) load,as well as the bending and torsional load on the top sub, and a triaxialaccelerometer 49 that senses vibration of the drill string. Usingtechniques well known in the art, the WOB can be calculated from thehook load measured by the strain gauges in the top sub, for example, bysubtracting the frictional resistance acting on the drill string fromthe measured hook load. The value of the frictional resistance can beobtained by pulling up on the drill string so that the drill bit is nolonger contacting the formation and noting the change in the hook load.In a wired pipe, the data from the downhole sensors would be received bythe top sub 45. The data from the top sub 45 strain gauges, as well asthe downhole sensors in a wired pipe system, can be transmitted viawireless telemetry to the surface acquisition system 12 using thetechnique disclosed in U.S. application Ser. No. 12/389,950, filed Feb.20, 2009, entitled “Synchronized Telemetry From A Rotating Element,”hereby incorporated by reference in its entirety.

Preferably, the surface monitoring system also includes a hook loadsensor 30 for determining WOB. The hook load sensor 30 measures thehanging weight of the drill string, for example, by measuring thetension in the draw works cable using a strain gauge. The cable is runthrough three supports. The supports put a known lateral displacement onthe cable. The strain gauge measures the amount of lateral strain due tothe tension in the cable, which is then used to calculate the axialload. A sensor 32 is also used for sensing drill string rotationalspeed.

3. Data Transmission and Processing

The drilling operation according to the current invention also includesa mud pulse telemetry system, which includes a mud pulser 5 incorporatedinto the downhole assembly 6. Using techniques well known in the art,the mud pulse telemetry system encodes data from downhole equipment,such as vibration information from the Vibration Memory Module™, and,using the pulser 5, transmits the coded pulses to the surface. Mud pulsetelemetry systems are described more fully in U.S. Pat. No. 6,714,138,entitled “Method And Apparatus For Transmitting Information To TheSurface From A Drill String Down Hole In A Well,” U.S. Pat. No.7,327,634, entitled “Rotary Pulser For Transmitting Information To TheSurface From A Drill String Down Hole In A Well,” and U.S. PatentApplication Publication No. 2006/0215491, entitled “System And MethodFor Transmitting Information Through A Fluid Medium,” each of which isincorporated by reference herein in its entirety.

According to the current invention, to reduce data transmissions, data,such as vibration information, may be grouped into ranges and simplevalues used to represent data in these ranges. For example, vibrationamplitude can reported as 0, 1, 2 or 3 to indicate normal, high, severe,or critical vibration, respectively. One method that may be employed toreport frequency is to assign numbers 1 through 10, for example, tovalues of the vibration frequency so that a value of 1 indicates afrequency in the 0 to 100 hz range, a value of 2 indicates frequency inthe 101 to 200 hz range, etc. The mode of vibration may be reported byassigning a number 1 through 3 so that, for example, a value of 1indicates axial vibration, 2 indicates lateral vibration, and 3indicates torsional vibration. If only such abbreviated vibration datais transmitted to the surface, at least some of the data analysis, suchas the Fourier analysis discussed below in connection with the use ofbackward whirl frequency to determine the borehole diameter, would beperformed in a processor installed in the bottom hole assembly.

As is also conventional, a data acquisition system 12, such as aSureShot™ system, discussed above, at the surface senses pressurepulsations in the drilling mud 14 created by the mud pulser 5 thatcontain encoded information from Vibration Memory Module™ and othersensors in the bottomhole assembly 6. The data acquisition system 12decodes this information and transmits it to a computer processor 18,also preferably located at the surface. Data from the surface sensors,such as the hook load sensor 30, the drill string rotational speedsensor 32, and the 34 are also transmitted to the processor 18.

Software 20, which includes the WellDrill™ software and stick-slipsoftware discussed above, as well as software for performing the methodsdescribed herein, discussed below, is preferably stored on anon-transitory computer readable medium, such as a CD, and installedinto the processor 18 that executes the software so as to perform themethods and functions discussed below. The processor 18 is preferablyconnected to a display 19, such as a computer display, for providinginformation to the drill rig operator. A data entry device 22, such as akeyboard, is also connected to the processor 18 to allow data to beentered for use by the software 20. A memory device 21 is incommunication with the processor 18 so that the software can send todata to, and receive data from, storage when performing its functions.The processor 18 may be a personal computer that preferably has at leasta 16× CD-ROM drive, 512 MB RAM, 225 MB of free disk space, a graphicscard and monitor capable of 1024×786 or better at 256 colors and runninga Windows XP™ operating system. Although the processor 18 executing thesoftware 20 of the current invention is preferably located at thesurface and can be accessed by operating personnel, portions of thesoftware 20 could also be installed into a processor located in thebottomhole assembly so that some of the operations discussed below, suchas a Fourier analysis of vibration data, could be performed downhole.

B. Software 1. Drill String Modeling

As discussed more fully below, the current invention makes use of theWellDrill™ software, discussed above. WeIIDrill™ can be employed inperforming the methods of the current invention because it does a muchbetter job of modeling the sources of vibration and the excitationforces than other programs. Most other programs predict the fundamentalnatural frequencies and base the mode shapes on this but do not takeinto account the whether the amplitudes and accelerations are sufficientto cause damage. WellDrill™ relies on a forced harmonic analysis thataccurately models the excitation forces and their applied frequencies.It also considers additional sources of vibration such as mud motorimbalances, bent collars and drill string imbalances.

The operation of the system for monitor and controlling the drillingoperation according to the invention is shown in FIG. 5A. In step 100,the operator begins by specifying the significant drill stringcomponents—such as a Measurement While Drilling (“MWD”) tool—and thevibration limits applicable to each such component. This information isinput into the WellDrill™ software, discussed above, in step 102 alongwith data on the bottomhole assembly. The data input into WellDrill™ mayinclude:

-   -   (i) the outside and inside diameters of the drill pipe sections        that make up the drill string,    -   (ii) the locations of stabilizers,    -   (iii) the length of the drill string,    -   (iv) the inclination of the drill string,    -   (v) the bend angle if a bent sub is used,    -   (vi) the material properties, specifically the modulus of        elasticity, material density, torsional modulus of elasticity,        and Poisson's ratio,    -   (vii) the mud properties for vibration damping, specifically,        the mud weight and viscosity,    -   (viii) the bore hole diameters along the length of the well,    -   (ix) the azimuth, build rate and turn rate,    -   (x) the diamter of the drill bit and stabilizers, and    -   (xi) information concerning the characteristics of the        formation, such as the strike and dip.

The information on the drill string components can also be updated bythe operator each time a new section of drill string is added. Asdiscussed above, data are also entered into the WellDrill™ softwarespecifying the expected operating parameters, such as those for (i) theWOB, (ii) the drill string RPM, (iii) the mud motor RPM, (iv) thediameter of the bore hole, and (v) the damping coefficients. In step 102the WellDrill™ software also performs a static bending analysis in whichit calculates the BHA deflections, the side forces along the length ofthe BHA, the bending moments and the nominal bending stress, as well asa “predict analysis” in which it uses the bending information to predictthe direction in which the drill string will drill.

In step 104, the software calculates vibration warning limits forspecific components based on the data from the sensors in the VibrationMonitoring Module™. For example, as discussed below, based on thepredicted mode shapes, the software can determine what level of measuredvibration at the accelerometer locations would result in excessivevibration at the drill string location of a critical component. In steps108 and 109, the software receives data from the rig surface anddownhole sensors so that such data can be used by the software on anon-going basis during the drilling operation, as discussed below. Datafrom the surface sensors are preferably transmitted to the system 12continuously. Data from the downhole sensors are transmitted to thesystem 12 whenever data are sent to the surface, preferably at leastevery few minutes. In step 110, data and status are transmitted to aremote server to allow users who are not at the well site to downloadand review the data, for example by logging into the server via theinternet. In step 112, the software determines whether any of thedrilling parameters input into WellDrill™ have changed and, if so, itupdates the WellDrill™ inputs and the model is revised accordingly.

FIG. 5B shows the method of creating the model of the drill string usingthe WellDrill™ software. In steps 260 to 272, the components of thedrill string are modeled using the ANSYS finite element technique, aspreviously discussed.

The aforementioned static bending analysis and predict analysis areperformed in steps 274 to 280. In step 282, the software determineswhether the forces are balanced at the bit—that is, whether the sideforces on the bit are equal to zero. If the forces are not balanced,then in step 284 the curvature of the borehole is modified and steps 272to 282 re-run until a balance is obtained in step 282. In steps 286 to294, a vibration analysis is performed by applying the drilling excitingforces to the model over a harmonic sweep and the resulting displacementalong each portion of the drill string is analyzed to determine thecritical speeds.

Thus, the WellDrill™ model is set up by first defining those drillstringand the well parameters that are not subject to changing during the run.These are stored by the software. As certain drilling conditions changethese are modified in the WellDrill™ program and the analysis re-run.Variables that change during drilling include: RPM, WOB, inclination,depth, azimuth, mud weight, and bore hole diameter. The model is updatedas the operating conditions change. Thus, unlike what was done in thepast, according to the current invention, the WellDrill model isautomatically updated based on real-time values of operating parametersbased on the measurements of the surface and down hole sensors. Asexplained below, the WellDrill™ software then calculates the criticalspeeds for a range of WOBs. These are displaced on a Critical Speed Map.The Critical Speed Map has RPM on the x-axis and WOB on the y-axis, andis therefore useful for a combination of conditions. Mode shapes at anygiven RPM and WOB combination can also be displayed.

2. Real-time Determination of Bore Hole Size

As discussed above, in the past the bore hole diameter used in theWellDrill model was base on an assumed value input by the operator,taking into account the diameter of the drill bit and type of formation.In the preferred embodiment of the invention, the real-time boreholediameter used in the model is calculated by the software 20 from thebackward whirl frequency. The backward whirl frequency can be calculatedas follows:

BWF=(d×w)/(D−d)

Where:

-   -   BWF=backward whirl frequency.    -   D=borehole diameter.    -   d=diameter of the drill bit or the diameter of another component        if the static bending analysis preformed by the WellDrill™        software determined that such other component was contacting the        bore hole wall.    -   w=rotary speed of the drill bit (for bit whirl) or the drill        string (for drill string whirl)

Therefore, if the whirl frequency is known, the diameter of thereal-time borehole can be calculated from the equation:

D=d×(1+w/BWF)

The software 20 determines the backward whirl frequency by performing aFourier analysis of the burst output of the lateral accelerationaccelerometer 44, with the backward whirl frequency taken to be thefrequency at which the Fourier analysis depicts a peak at or near thepredicted whirling frequency. The expected whirling frequency caninitially be estimated from the equation above, using the bit diameterand the expected bore hole diameter. Such a Fourier analysis can beperformed by the processor 18 at the surface after the vibration datahas been transmitted to the surface by either a mud pulse telemetrysystem or a wired pipe or other transmission system, as previouslydiscussed. Alternatively, the Fourier analysis could be performeddownhole by incorporating into the BHA, for example into an MWD tool, aprocessor programmed, using techniques well know in the art, to performFourier analyses. The vibration data necessary to perform the Fourieranalysis of the lateral vibration accelerometer output would betransmitted to the downhole processor by the Vibration Memory Module™.

3. Prediction of Critical Speeds

As indicated in connection with step 102, using Welldrill™, the software20 performs a vibration analysis in which it predicts (i) the naturalfrequencies of the drill string in axial, lateral and torsional modesand (ii) the critical speeds of the drill string, mud motor (if any),and drill bit that excite these frequencies, as previously discussed.However, unlike what was done in the past, the software 20 also adjuststhe WellDrill™ model if the actual critical speeds don't match theprediction so that the model correctly predicts the critical speedsexperienced by the drill string. The method shown in FIG. 6 can be usedto adjust the model if it predicts a critical speed at an RPM thatactual operation reveals does not result in resonant vibration. If acritical speed is encountered at an RPM at which the WellDrill™ modeldoes not predict resonant vibration, then the model can be adjustedusing the method discussed in section 9 after the successful eliminationof high vibration that caused a loss of drilling performance.

As shown in FIG. 6, the software first determines in step 330 whether apredicted critical speed differs from a measured critical speed by morethan a predetermined amount if it does, in step 332, the softwaredetermines whether the vibratory mode associated the critical speed wasrelated to the axial, lateral or torsional vibratory mode. If thecritical speed was associated with the torsional or axial modes, then instep 334 the software determines if the RPM at which the mud motor isthought to be operating, without encountering the predicted resonantvibration, is on the lower end of the predicted critical speed band. Ifit is, then in step 336 the motor RPM used by the model is decreaseduntil the critical speed is no longer predicted. If it determines thatthe motor RPM is on the upper end of the predicted critical speed band,then in step 338 the motor RPM is increased until the critical speed isno longer predicted. If the mud motor is not being used, then in step340 the software determines whether the predicted critical speed ishigher or lower than the speed at which the drill bit is operating. Ifit is higher, then in step 342 the drill string stiffness is decreaseduntil the critical speed is no longer predicted. If it is lower, then instep 344, the drill string stiffness is increased until the criticalspeed is no longer predicted.

if the critical speed was associated with the lateral vibratory mode,then in step 346 the software determines if the lateral vibration is dueto drill bit, mud motor, or drill string lateral vibration. If thelateral vibratory mode is associated with the drill string, then in step348 the software determines whether the RPM at which the drill string isthought to be operating, without encountering resonance, is on the loweror higher end of the predicted critical speed band. If it is on the highend, then in step 350 the drill string speed used in the model isreduced or, if that is unsuccessful, a stabilizer OD is increased. If itis on the low end, then in step 352 bore hole size used in the model isincreased or, if that is unsuccessful, the OD of a stabilizer isdecreased.

If the lateral vibratory mode is associated with the mud motor, then instep 354 the software determines whether the RPM at which the mud motoris thought to be operating, without encountering resonant vibration, ison the lower or higher end of the predicted critical speed band. If itis on the high end, then in step 356 the mud motor speed used in themodel is increased until the critical speed is no longer predicted. Ifit is on the low end, then in step 358 the mud motor speed used in themodel is decreased until the critical speed is no longer predicted. Ifthe lateral vibratory mode is associated with the drill bit, then instep 360 the software determines whether the RPM at which the drill isthought to be operating is on the lower or higher end of the criticalspeed band. If it is on the high end, then in step 362 the drill bitspeed is decreased until the critical speed is no longer predicted. Ifit is on the low end, then in step 364 the drill bit speed is increaseduntil the critical speed is no longer predicted.

4. Prediction of Vibration and Extrapolation of Measured Vibration toVibration at Critical Components

As also indicated in connection with step 102, using WellDrill™,discussed above, the software 20 performs vibration analyses, includingpredicting the mode shapes resulting from axial, lateral and torsionalvibration based on the current measured operating parameters. Althoughthe software 20 uses WellDrill™ to predict vibration and calculate themode shapes, unlike what was done in the past, the software of thecurrent invention automatically determines the mode shape at themeasured values of the real-time operating parameters.

In the preferred embodiment, the software predicts vibration at eachelement along the drill string based on the real time values of (i) WOB,(ii) drill bit RPM, (iii) mud motor RPM, (iv) diameter of borehole, (v)inclination, (vi) azimuth, (vii) build rate, and (viii) turn rate. Forpurposes of predicting vibration, WOB is preferably determined fromsurface measurements using the top drive sub 45, as previouslydiscussed, although downhole strain gauges could also be used as alsopreviously discussed. Drill bit RPM is preferably determined by summingthe drill string RPM and the mud motor RPM. The drill string RPM ispreferably based on a surface measurement using the RPM sensor 32. Themud motor RPM is preferably based on the mud flow rate using a curve ofmud motor flow rate versus motor RPM or an RPM/flow rate factor, aspreviously discussed. The diameter of the bore hole is preferablydetermined from the backward whirl frequency as discussed in section 2above, although an assumed value could also be used, as also previouslydiscussed. Inclination and azimuth are preferably determined fromaccelerometers 44 and magnetometers 42 in the BHA, as previouslydiscussed. Build rate is preferably determined based on the change ininclination. Turn rate is determined from the change in azimuth.Preferably, the information on WOB, drill string RPM and mud motor RPMis automatically sent to the processor 18 for use by the software 20 bythe SureShot™ surface system, discussed above, information oninclination and azimuth, as well as data from the lateral vibrationaccelerometers (the backward whirl frequency if the Fourier analysis isperformed downhole), are transmitted to the processor 18 by the mudpulse telemetry system or a wired pipe or other transmission system atregular intervals or when requested by the software 20 or when triggeredby an event.

According to the current invention, three oscillating excitation forcesare used to predict vibration levels: (i) an oscillating excitationforce the value of which is the measured WOB and the frequency of whichis equal to the speed of the drill bit multiplied by the number ofblades/cones on the bit (this force is applied at the centerline of thebit and excites axial vibration), (ii) an oscillating force the value ofwhich is the measured WOB and frequency of which is equal to the numberof vanes (or blades) on drill bit times the drill bit speed (this forceis applied at the outer diameter of the bit and creates a bending momentthat excites lateral vibration), and (iii) an oscillating force thevalue of which is the calculated imbalance force based on thecharacteristics of the mud motor, as previously discussed, and thefrequency of which is the frequency of which is equal to N (n+1), whereN is the rotary speed of the rotor and n is the number of lobes on therotor.

Based on the foregoing. WellDrill calculates the amplitude and frequencyof the vibration at teach point along the drill string. A plot of suchdata, such as that shown in FIG. 7 shows, for the current operatingcondition, the vibratory mode shape of the drill string, which isessentially the relative amplitude of vibration along the drill string.

Vibration amplitude is measured only at the locations of vibrationsensors, such as accelerometers. However, of importance to the operatoris the vibration at the location of critical drill string components,such as an MWD tool. Since the software 20 predicts mode shape, andknows the location of such critical components, in step 104 itdetermines the ratio between the amplitude of vibration at a nearbysensor location and the amplitude of vibration at the critical componentfor each mode of vibration. Based on the inputted vibration limit forthe component, it determines the vibration at the sensor that willresult in the vibration at the component reaching its limit. It willthen issue a high vibration alarm if the vibration at the sensor reachesthe correlated limit. For example, if the maximum vibration to which anMWD tool should be subjected is 5 g and the mode shape analysisindicates that, for lateral vibration, the ratio between the vibrationamplitude at sensor #1 and the MWD tool is 1.5—that is, the amplitude ofthe vibration at the MWD tool is 1.5 times the amplitude at sensor #1,the software would advise the operator of the existence of highvibration at the MWD tool if the measured lateral vibration at sensor #1exceeded 1.33 g. This extrapolation could be preformed at a number oflocations representing a number of critical BHA components, each withits own vibration limit.

In addition to predicting vibration along the length of the drill atcurrent operating conditions in order to extrapolate measured vibrationamplitudes to other locations along the drill string, the software canalso predict vibration along the length of the drill string based onprojected operating conditions so as to allow the software to determinewhether a change in operating parameters, such as RPM or WOB, willaffect vibration.

5. Prediction of Torque and Stick-Slip and Extrapolation of MeasuredTorque to Torque at Critical Components

Using the methodology discussed above, the vibration analysis performedin step 102 also includes a calculation of the torque at each sectionalong the drill string and a prediction as to when stick-slip willoccur. For stick-slip, torque is the important load as this may resultin connections over-torquing, backing off, or unscrewing due to theoscillating torsion loads. In addition to analyzing torsional vibrationduring drilling, the software analyzes the operating parameters todetermine if an over-torquing or reverse over-torquing situation isoccurring at any location along the length of the drill string.

Due to vibrations and stick-slip conditions, the RPM along the drillstring varies. The long length of the drill string, along with theapplied torque at the bit and on the drill string, will result in thedrill string winding up many times between the surface and the bit.Vibrations and stick-slip conditions result in the drill stringoscillating along its length. The drill string may be rotating at agiven RPM at one location and rotating at a different RPM at otherlocations along its length. The drill string may stop rotating at somelocations and even rotate in the reverse direction.

In a preferred embodiment, the instantaneous RPM is measured usingmagnetometers in the BHA, which measure RPM at 400 Hz. Preferably, thesoftware advises the operator if the these readings indicate excessivevariation in instantaneous RPM. In particular, RPM is calculated by thephase change to earth's magnetic field as seen by the magnetometer. Themagnetometers measure the phase change of the earth's magnetic field asthe magnetometer rotates within the drill collar. The magnetometermeasures the angular position of the collar at a given time. Thereforethe change in angular position is measured from one time step to thenext.

The WellDrill™ software is used to predict the oscillating angulardisplacement (θ) at positions along the length of the drill string usingfinite element techniques for forced vibration such as theBernoulli-Euler beam theory. In the preferred embodiment, the maximumtorque at the bit is assumed to be calculated from the WOB×the bitradius×a bit factor. The bit factor is the ratio of the torsional forcegenerated by the cutters/WOB. The oscillating frequency is assumed to bethe rpm of the drill string×the number of cutters or blades on the bit.The minimum force is assumed to be 0 torque. However other torque rangesmay be used.

Stick-slip is also a source of oscillating torque. Finite differenceequations, discussed above in the section entitled Stick-Slip Software,are used to calculate the angular displacements at time intervals alongthe length of the drill string. The angular displacement along thelength of the drill string is the combined static displacement due tobit torque and drag torque with the oscillating torque. (The value ofthe full bit torque can be obtained from information provided by the bitsupplier, such as drill bit torque itself or a bit factor, which is theratio of the bit torque to WOB.) The value for the oscillating RPMpredicted at the location of the magnetometer in the bottom holeassembly is then compared to the oscillating RPM data from themagnetometer itself. If the two values do not agree within apredetermined amount, for example 10%, then the methodology discussedbelow in connection with FIG. 11 (whirl) is used to adjust theWellDrill™ model and the analysis is re-run.

The WellDrill™ software also calculates the steady torque along thelength of the drill string based on the applied torque at the bit andfriction drag effects along the drill string. The WOB, inclination,build and turn rates affect the gravity effects on the tool, which, inturn, determine the amount of drag along the length of the drill stringand, in turn, the torque along the drill string. Combining both thesteady torque and the vibratory torque yields the maximum torqueexperienced at each element of the drill string.

Based on the angular displacements along the drill string calculated asdiscussed above, the software determines the torque at each locationalong the drill string from the equation:

T=(Δθ×J×G)/L

Where:

-   -   Δθ=the angular displacement across each element    -   G=the shear modulus of the element    -   J—the polar moment of inertia of the element    -   L=the length of the element

If a WTB sub, as described above, is used, the torque at a specificlocation is directly measured, for example, by the strain gauges in theWTB sub as discussed in the aforementioned U.S. Pat. No. 6,547,016incorporated by reference above. Use of a top sub, also described above,will result in the measurement of the torque at the surface. If neithera top sub nor a WTB sub is used, then the torque at the Vibration MemoryModule™ can be calculated by the change in instantaneous speed and themass at that section.

Regardless of how toque is measured, using the prediction of torquealong the length of the drill string, the software extrapolates thetorque at the measured location to other locations along the length ofthe drill string. For example, based on the torque predicted byWellDrill™ for the operating parameters being experienced, the torque ata particular drill pipe joint may be predicted to be 1.5 time greaterthan at the WTB sub. The torque value measured at the WTB sub would thenbe increased by a factor of 1.5 to predict the toque at the pipe joint.

Allowable torque limits for critical drill string components can beinput into the software 20 and stored in the memory 21 of the processor18. Such limits are usually available from piping, heavy weight anddrill collar specifications. During operation, the software 20 comparesthe predicted value of the torque at the critical locations to the limitset for the components at those location to determine if an over-torquecondition exists and, if so, it alerts operating personal. In someembodiments of the invention, if the software also determines thatstick-slip is occurring, for example, using the methodology discussedbelow in section 7 concerning the identification of causes of lostdrilling performance (e.g., high torsional vibration at a frequency lessthan 1×bit speed), it would automatically adjust the operatingparameters as shown in FIG. 10 until the torque was reduced below thelimit.

According to the current invention, as an alternative to the finiteelement method used by WellDrill™ discussed above, torque along thedrill string can also be predicted using the finite differencemethodology discussed above in the section entitled Stick-Slip Software,with the torque applied to each section being equal to the incrementalmoment ΔM=μ F_(n) r. Using that alternative, the software compares thepredicted values for torque at the measured locations to the measuredvalues and adjusts the model so that the predicted values at themeasured locations agree with the measured values. Such adjustment canbe accomplished by varying the sliding coefficient of friction, used bythe software.

6. Critical Speed Map

As discussed above, the software 20 creates a drill string model thatallows it to predict the vibration level at each point along the drillstring for every combination of WOB, drill string RPM, and mud motorRPM. Using the software discussed above in the section entitled“Stick-Slip Software”, the software 20 also whether stick-slip willoccur at every combination of WOB and drill string RPM Based on thesepredictions, the software displays critical speed maps, an example ofwhich is shown in FIG. 8, indicating the combinations of WOB and drillstring RPM that should be avoided to avoid high axial or lateralvibration or stick slip. Another critical speed map indicates thecombinations of WOB and mud motor RPM that should be avoided. Thecritical speed maps are displayed to the operator, for example on theCRT screen 19, as a guide for setting drilling parameters.

7. Identifying Causes of Lost Performance

In a preferred embodiment, the software 20 according to the inventionincludes an expert system that identifies the causes of lost drillingperformance and, in some embodiments, makes recommendations to theoperator for mitigating the lost performance. In still otherembodiments, the software automatically adjusts certain predeterminedoperating parameters to minimize such lost performance. Preferably, thesoftware relies on a data base, which may be stored in memory 21, thatcorrelates a set of predetermined causes of lost drilling performance Xwith a set of predetermined symptoms of lost performance Y on the basisof probabilities—that is, the probably P_(xy) that cause of lostdrilling performance X will manifest itself in the presence of symptomY. Such a data can be created, for example, based on experience withsimilar drilling operations or based on analysis of data from thesubject drilling operation. Table I shows a correlation relating theprobabilities P_(xy) that causes of lost performance X₁ through X_(n)will manifest themselves in the appearance of symptoms Y₁ through Y_(m).

TABLE I Causes of lost Symptoms of Lost Performance performance Y₁ Y₂ Y₃. . . Y_(m) X₁ P₁₁ P₁₂ P₁₃ . . . P_(1m) X₁ P₂₁ P₂₂ P₂₃ . . . P_(2m) . .. . . . . . . . . . . . . . . . X_(n) P_(n1) P_(n2) P_(n3) . . . P_(nm)

As an example, Table II is a correlation showing the probability P_(xy)that a cause of lost performance X will manifest itself as symptom Y,where the causes of lost performance are vibration (X₁), problems withthe drill bit (X₂), problems with the bottomhole assembly (“BHA”) (X₃),and difficulties created by the formation (X₄), and the symptoms of lostperformance are those which manifest themselves as vibration (Y₁),downhole dynamics (Y₂), operating conditions (Y₃), phenomenonmeasureable by rig floor and top drive sensors (Y₄), and mattersconcerning the well profile (Y₅).

TABLE II Symptoms of Lost Performance, Y Rig Floor & Causes of lostVibra- Downhole Operating Top Drive Well performance, X tion DynamicsConditions Sensors Profile Vibration P₁₁ P₁₂ P₁₃ P₁₄ P₁₅ Drill Bit P₂₁P₂₂ P₂₃ P₂₄ P₂₅ BHA P₃₁ P₃₂ P₃₃ P₃₄ P₃₅ Formation P₄₁ P₄₂ P₄₃ P₄₄ P₄₅

As shown in FIG. 9, during the drilling operation, the softwaredetermines the most likely cause of lost performance X_(max) byanalyzing the data generated by various sensors to determine whichsymptoms of lost performance Y_(a) are present, and then summing theprobabilities associated with those symptoms for each cause of lostperformance X_(b) to identify the cause of lost performance exhibitingthe highest probability of being present. In steps 200-208, the softwaregoes through each of a pre-determined list of symptoms of lost drillingperformance Y_(a) and compares the sensor data to criteria set for eachsymptom to determine whether the symptom is deemed to be present. Forexample, one symptom of lost drilling performance is fluctuating WOB,the presence of which correlates well with high axial vibration (bitbounce) and, to a lesser extent, stringers in the formation andstick-slip. The criteria for determining that such fluctuating WOB ispresent might be fluctuations of at least 50%. Accordingly, the softwarewill analysis the data from the WOB sensor and determine whether thecriteria for fluctuating WOB are satisfied—that is, whether thefluctuations exceed 50%—and, if so, it will flag fluctuating WOB as asymptom of lost drilling performance that is present in the data.

In step 210, the software goes through each of a pre-determined list ofcauses of lost drilling performance X_(b) and, by querying the data basecorrelating probabilities that the specified causes of vibration will bemanifested in the specified symptoms, retrieves the probability thateach symptom found to be present is the result of such cause. Forexample, the data base may indicate that (i) whirl type vibration has a10% probability of causing fluctuating WOB, (ii) bit bounce has a 100%probability of causing fluctuating WOB and (iii) stick-slip has a 50%probability of causing fluctuating WOB. If fluctuating WOB were deemedto be present, each of these probabilities would be retrieved.

In step 212, the probabilities associated with each symptom of lostdrilling performance deemed to be present are summed for each potentialcause of lost performance. For example, in addition to fluctuating WOB,another symptom of lost drilling performance might be a decrease invibration as a result of an increase in WOB. If the sensor dataindicates that this symptom is also present, and the data base indicatesthat bit bounce has a 30% probability of manifesting itself as adecrease in vibration as a result of an increase in WOB, then the 30%probability associated with a decrease in vibration resulting from anincrease in WOB is added to the 100% probability associated withfluctuating WOB so that the accumulating probability of bit bouncebecomes 130%. In step 214, the cause of lost drilling performance withthe maximum total probability, X_(max), is identified.

A simple version of a data base for three vibration-related causes oflost performance and thirteen symptoms of lost performance is shown inTable III.

TABLE III Symptoms of Loss Performance Causes of Vibration OperatingConditions lost Frequency Downhole Increase Increase Increaseperformance Amplitude (No. Dynamics RPM WOB flowrate associated HighHigh cones/no. Multiple Less than Fluc- High Vib Vib Vib Vib Vib Vibwith lateral axial blades) × of bit 1X rotary tuating bending in- de-in- de- in- de- vibration vibration vibration bit speed speed speed WOBstress creases creases creases creases creases creases Backward 80 0 7030 0 10 40 80 0 50 0 0 0 Whirl Bit Bounce 0 60 80 20 0 100 0 20 0 0 30 00 Stick-slip 10 0 0 0 100 0 0 0 80 80 0 0 0

Table III shows the probabilities that each of three vibration-relatedcauses of lost drilling performance—backward whirl, bit bounce andstick-slip—will manifest itself as each of thirteen symptoms of lostperformance, grouped into three categories—vibration downhole dynamicsand operating conditions. For example, experience may show that there isan 80% probability that backward whirling will result in a very high(i.e., severe) amplitude of lateral vibration, a 70% probability thatbackward whirl will result in vibration having a frequency equal to thenumber of cones on the drill bit times the number of blades divided bythe bit speed, etc. By contrast, experience may show that there is 0%probability that bit bounce will result in very high lateral vibrationbut a 60% probability that it would result in high axial vibration.

At each data gathering interval, the software will determine thepresence of the various symptoms and then calculate which cause of lostperformance is most likely occurring by adding up the probabilities. Inthe example shown in. Table IV, analysis of the data from the vibrationsensors indicates that high lateral vibration is present at a frequencythat is equal to the number of cones on the drill bit divided by thenumber of blades on the drill bit multiplied by RPM of the drill bit.The vibration sensor data does not indicate that high axial vibration ispresent or that the frequency of the vibration is either a multiple ofdrill bit RPM or less than one times the drill string RPM. With respectto downhole dynamics, analysis of the WOB sensor indicates that the WOBis not fluctuating, whereas analysis of the data from strain gauges onthe drill collar indicates that the bending stress on the drill bit ishigh. With respect to operating conditions, comparison with prior setsof data indicate that an increase in drill bit RPM resulted in anincrease in vibration but that an increase in WOB resulted in decreasedvibration and that an increase in mud flow rate resulted in no change invibration. By retrieving and summing the probabilities associated witheach of these symptoms, obtained from the data base stored in memory,the software determines that the most likely cause of lost performanceis backward whirl, as shown by the “Total Score” in Table IV.Preferably, the software performs such an analysis each time a set ofdata are transmitted up hole via the mud pulse telemetry system, wiredpipe or other transmission system, which may be as often as every fewminutes.

TABLE IV Symptoms of Lost Performance Vibration Causes of FrequencyOperating Conditions lost Vib. Mul- Less Downhole Increase IncreaseIncrease performance Amplitude freq. = (no. ti- than Dynamics RPM WOBflowrate associated High High cones/no. ple 1X Fluc- High Vib Vib VibVib Vib Vib with lateral axial blades) × of bit rotary tuating bendingin- de- in- de- in- de- Total vibration vibration vibration bit speedspeed speed WOB stress creases creases creases creases creases creasesscore Condition X X X X X Present? Backward 80 70 40 80 0 270 Whirl BitBounce 0 80 0 20 30 130 Stick-slip 10 0 0 0 0 10

Table V shows a more extensive listing of the causes of lost performancepreferably used in the software.

TABLE V Causes of Lost Performance Vibration Drill Bit BHA Formation Bitbackward whirl Worn bit Buckling Stringers BHA forward whirl Damaged bitStabilizer balling Hole collapse BHA backward whirl Hole cleaningCracked collar Differential sticking Bit bounce Plugged bit Wash outLedges Mud motor vibration Junk in hole Undergauge stabilizer Enlargedhole Stick-slip Bit balling Insufficient hole cleaning BRAimbalance/bent collar Collar/bore hole contact Agitator Jars fired Motorstator damage Motor bearing damage Mud motor wear

Tables VI, VII and VIII show more extensive listings of the symptoms oflost performance. The symptoms involving “MSE” in Table VIII refer tothe “Mechanical Specific Energy” calculated as discussed in section 11,below, concerning optimization of drilling efficiency.

TABLE VI Vibration-Related Symptoms of Lost Performance AmplitudeFrequency Severe/high lateral vibration Less than 1X bit speedSevere/high axial vibration 1X bit speed Severe/high torsional vibration(No. cones/blades) x bit speed Multiple of bit speed Less 1X drillstring speed 1X drill string speed Multiple of drill string speed No.lobes of mud motor x motor speed

TABLE VII Downhole Operating Conditions Related Symptoms DynamicsRelated Increasing RPM Increasing WOB Increasing mud Symptoms causescauses flow rate causes Low WOB Increased vibration Increased vibrationIncreased vibration High WOB Decreased vibration Decreased vibrationDecreased vibration Fluctuating WOB Unchanged vibration Unchangedvibration Unchanged vibration Low torque Vibration peak Vibration peakVibration peak High torque Sudden increase Sudden increase Suddenincrease Fluctuating torque Sudden decrease Sudden decrease Suddendecrease Low bending stress High bending stress Fluctuating bending

TABLE VIII Symptoms from Rig Floor/Top Drive Sensors Well ProfileRelated Symptoms ROP decline High build rate ROP increase Straight holeROP unchanged Tortuosity MSE increase Vertical hole MSE decreaseHorizontal hole MSE unchanged Poor directional control RPM fluctuationsWOB fluctuations Torque fluctuations Torque decrease Torque fluctuationsPressure increase Pressure decrease Pressure fluctuations

As an example, Table IX and X set forth one data set that may be used tospecify the percent probability that each identified symptom (listed inthe rows) is the result of the associated cause of lost performance(listed in the column headings), for the symptoms of lost performanceidentified in Tables VI, VII and VIII.

TABLE IX Causes of Lost Drilling Performance Insufficient Symptoms ofLost Drilling Stabilizer Cracked Wash Undergauge hole Collar/hole JarsMotor Motor Hole Differential Performance Buckling balling collar Outstabilizer cleaning contact Agitator fired stator bearing Stringerscollapse sticking Ledges Vib Severe/critical lateral vib 30 25 50 50 3030 30 10 30 Level Severe/critical axial vib 30 40 60 10 30 30Severe/critical torsional vib 20 10 10 30 40 50 High lateral vib 75 4070 70 75 60 60 30 70 High axial vib 80 100 30 70 80 High torsional vib40 30 30 70 80 90 Vib Less then 1x bit speed 80 80 Frequency 1x bitspeed 50 40 40 # cones/blades x bit speed 80 70 Multiple of bit speed 2030 Less than 1x rotary speed 1x rotary speed Multiple of rotary speed 6060 # lobes x motor speed WOB/ Low WOB 50 TOB/ High WOB BOB FluctuatingWOB 70 Low torque High torque 50 50 70 100 100 50 Fluctuating torque Lowbending High bending 60 80 30 Fluctuating bending 70 70 Increasing Vibstays same RPM Vib increases 50 40 30 40 30 50 30 Vib decreases 50 50 5030 Vib peaks 70 Comes on suddenly 30 60 30 Drops out suddenly 30Increasing Vib stays same 70 100 WOB Vib increases 30 40 50 60 30 Vibdecreases 40 30 70 Vib peaks Comes on suddenly 70 Drops out suddenly 60Increasing Vib stays same 100 Flow Vib stays same Rate Vib increases 5075 20 30 Vib decreases Vib peaks Comes on suddenly 20 Drops out suddenlyRig ROP decline 75 30 60 20 50 30 70 100 100 80 Floor/Top ROP increase50 Drive ROP unchanged 30 Sensors MSE increase 80 MSE decrease 75 20 6020 50 70 100 100 80 MSE unchanged 90 30 RPM fluctations 50 WOBfluctations 60 Torque increases 60 20 60 10 30 30 100 100 Torquedecreases 80 40 Torque fluctuations 50 40 Pressure increase 60 60 60 80Pressure decrease 70 100 40 Pressure fluctuations 20 50 Well High buildrate 80 50 Profile Straight hole Tortuousity 10 Vertical hole Horizontalhole 40 80 80 Poor directional control 10 30 40 40

TABLE X Causes of Lost Drilling Performance BHA BHA BHA Symptoms of LostDrilling Bit Backward forward backward Motor imbal/bend Hole PluggedJunk in Performance whirl whirl whirl Bit bounce vibration Stick-slipcollar Worn bit Damaged bit cleaning bit hole Bit balling Vib LevelSevere/critical lateral vib 80 30 80 50 20 20 20 40 30 Severe/criticalaxial vib 30 20 20 40 30 Severe/critical torsional vib 50 40 Highlateral vib 100 60 100 70 30 40 30 60 50 High axial vib 60 30 30 60 60High torsional vib 100 60 Vib Frequency Less then 1x bit speed 100 1xbit speed # cones/blades x bit speed 70 80 Multiple of bit speed 30 2050 50 Less than 1x rotary speed 100 50 1x rotary speed 50 100 Multipleof rotary speed 50 100 # lobes x motor speed 100 WOB/TOB/BOB Low WOB 20High WOB 60 Fluctuating WOB 10 10 100 50 40 Low torque 60 30 High torque40 20 50 60 70 60 30 30 30 Fluctuating torque 100 100 40 40 40 Lowbending High bending 40 60 50 60 50 Fluctuating bending 100 50 100 10020 Increasing Vib stays same 50 40 40 40 40 60 RPM Vib increases 80 8020 30 100 50 40 40 Vib decreases 80 Vib peaks 100 80 100 Comes onsuddenly 40 40 50 Drops out suddenly 20 50 50 Increasing Vib stays same20 30 40 50 60 WOB Vib increases 50 50 80 100 50 30 25 Vib decreases 7030 25 Vib peaks Comes on suddenly 70 40 50 50 Drops out suddenly 25 2540 Increasing Vib stays same 80 80 Flow Rate Vib stays same 30 Vibincreases 80 30 50 Vib decreases 70 Vib peaks Comes on suddenly Dropsout suddenly Rig Floor/Top ROP decline 75 20 75 20 40 75 20 100 100 7575 95 80 Drive Sensors ROP increase 50 ROP unchanged 25 40 20 20 MSEincrease 60 MSE decrease 75 30 75 20 40 90 100 100 60 60 95 80 MSEunchanged RPM fluctations 30 100 40 30 WOB fluctations 70 30 Torqueincreases 30 20 30 100 60 50 20 50 Torque decreases 80 50 70 Torquefluctuations 50 100 30 Pressure increase 30 100 40 Pressure decreasePressure fluctuations 40 Well Profile High build rate 30 Straight hole30 40 40 20 Tortuousity 30 Vertical hole 30 30 30 Horizontal hole 50Poor directional control 50 20 30 20 60 30 40 40

8. Eliminating the Cause of Lost Drilling Performance

In step 216, the software determines whether the maximum Total Score,X_(max), exceeds a predetermined threshold. If it does not, the softwaredetermines that no action need be taken to eliminate the identifiedcause of lost drilling performance. If, in step 216, the softwaredetermines that the Total Score exceeds the predetermined threshold, theresults of the foregoing analysis—that is, the most likely cause of lostdrilling performance—is displayed to the operator in step 218 so that hecan take remedial action. For example, if the analysis indicated thatthe most likely cause of lost performance was a worn drill bit, theoperator could schedule a replacement of the drill bit.

In a preferred embodiment of the invention, the software 20 providesrecommendations to the drill rig operator for eliminating the cause oflost drilling performance. For example, if the most likely cause of lostperformance was identified as a worn bit, the software will advise theoperator to decrease drill bit RPM or WOB in order to reduce the wear onthe bit. Similarly, if the cause of lost performance were insufficienthole cleaning, the software would advise the operator to increase theflow rate of drilling mud and reduce the WOB. Prior to providing arecommendation to the operator to adjust a drilling parameter, thesoftware determines whether such adjustment would result in highvibration by predicting the vibration that would result from suchoperation as discussed in section 4 or result in a stick-slip situationby performing the stick-slip analysis discussed in section 3 concerningthe creation of critical speed maps.

In step 217, the software determines whether or not the most likelycause of lost performance is vibration related. If the most likely causeof lost drilling performance is vibration-related, the software advisesthe operator as to how to mitigate such lost performance, as discussedbelow.

FIGS. 10-12 show one embodiment of a method for mitigating lost drillingperformance. In step 300, a determination is made as to the type ofvibration associated with the identified vibration-related cause of lostdrilling performance—for example, bit bounce, whirl or stick-slip. Ifthe software determined that the high vibration is due to stick-slip,steps 302-306 are performed, in which the software advises the operatorto increase drill bit RPM by a predetermined amount and then determineswhether such an increase in drill bit RPM reduces vibration below apredetermined maximum level associated with “normal” vibration. If theincrease in drill bit RPM caused the vibration to decrease but it wasstill above normal, the software would recommend another such decreasein RPM to the operator as indicated in step 306. If the vibration wasnot so reduced, steps 308-312 are performed, in Which the softwareadvises the operator to decrease WOB by a predetermined amount and thendetermines if such a decrease in WOB reduces vibration below thepredetermined maximum. If either procedure reduces vibration below thepredetermined maximum, the cause of lost drilling performance is deemedto have been mitigated. If software determines that neither procedure issuccessful, the operator is advised in step 314 that lost performance isnot vibration related so that the operator can investigate otherpotential sources of lost drilling performance.

If the cause of lost performance is whirl, steps 400-410, shown in FIG.11, are performed, in which the software advises the operator todecrease and then increase drill bit RPM and determines if such changesmitigates the whirl. If not, steps 412-422 are performed, in which thesoftware recommends to the operator to increase and then decrease theflow rate of drilling mud and determines if such changes mitigate thewhirl. If it does not, steps 424-428 are performed, in which thesoftware recommends to the operator to decrease WOB and determines ifsuch change mitigates the whirl. If the software determines none ofthese recommendations are successful, the operator is advised in step430 that lost performance is not vibration related so that the operatorcan investigate other potential sources of lost drilling performance.

If the cause of lost performance is bit bounce, steps 500-510, shown inFIG. 12, are performed, in which the software recommends to the operatorto increase and then decrease WOB and determines if such changesmitigate the bit bounce. If it does not, then steps 512-522 areperformed, in which the software recommends to the operator to increaseand then decrease drill bit RPM and determines if such change mitigatesthe bit bounce. If the software determines that none of these proceduresare successful, the operator is advised in step 524 that lostperformance is not vibration related so that the operator caninvestigate other potential sources of lost drilling performance.

As previously discussed in connection with the creation of a criticalspeed map, the software 20 predicts the drill bit RPM, WOB and mud motorRPM that will result in excessive vibration due to resonance orstick-slip. Although not illustrated in the flow charts shown in FIGS.10-12, prior to recommending any change in drill bit RPM, WOB, ordrilling mud flow rate, the software will predict whether theanticipated change will increase vibration, and especially whether itwould result in operation at a critical speed. If the predictionindicated that the anticipated change would drive operation into an areaof high vibration, the software would not recommend that change and thenext vibration-related mitigation procedure would be recommendedinstead.

In the foregoing, the predetermined increments by which the amounts thedrill bit RPM, WOB and drilling mud flow rate are increased or reducedmay be about 5% for each increase/decrease, although greater or lesseramounts could also be used. The preferred embodiment of the method ofmitigating vibration-related lost drilling performance discussed aboverelies on procedures believed by the inventors to most likely mitigatevibration so as to avoid unnecessary changes in operating parameters.For example, decreasing drill bit RPM or increasing WOB are not believedto be fruitful in attempting to mitigate stick-slip and, therefore, suchchanges are not effected in the methodology illustrated in FIG. 10.However, other changes in operating parameters could be incorporatedinto the method to mitigate vibration if experience showed them to befruitful.

In some embodiments, instead of merely recommending changes that theoperator makes to the operating parameters, the method described in theflowcharts shown in FIGS. 10-12 could be implemented by the softwareautomatically changing the operating parameters. For example, toincrease the drill bit RPM, the software would cause the processor tosend a signal to the motor controller of the motor operating the topdrive causing it to increase the motor speed of the top drive and,therefore, the RPM of the drill string. To increase the mud flow rate,the software would cause the processor to send a signal to thecontroller of the motor operating the mud pump causing it to increasethe motor speed and, therefore, the mud flow. Similarly, to reduce theWOB, the software would cause the processor to send a signal to themotor controller of the motor that controls the draw works cablescausing them to decrease the WOB.

9. Correcting the Model to Reflect Measured Vibration Levels

As discussed above, the software 20 has access to (i) the measuredaxial, lateral and torsional vibration at the locations of theaccelerometers, supplied by the Vibration Memory Module™, (ii) theresonant frequencies for the axial, lateral and torsional vibrationpredicted by the WellDrill™ software, (iii) the mode shapes for theaxial, lateral and torsional vibration based on real-time operatingparameters predicted by the WellDrill™ software, and (iv) the levels ofaxial, lateral and torsional vibration at each point along the entirelength of the drill string predicted by the WellDrill™ software.According to the invention, each time a set of data is received from thedownhole sensors, the software 20 compares the measured level ofvibration at the accelerometer locations to the predicted level ofvibration at these same locations. If the software 20 determines thatthe difference between the predicted and measured vibration for any ofthe axial, lateral or torsional vibrations at accelerometer locationsexceeds a predetermined threshold, it revises the model by varying theoperating parameter inputs used in the model, according to apredetermined hierarchy, until the difference is reduced below thethreshold.

Preferably, if the checking of predicted versus measured vibration isperformed by the software following a successful mitigation of highvibration, discussed above, the results of the mitigation are used toguide the revision of the model used to predict the vibration, as shownin FIG. 13. In step 600, the amplitude of the measured vibration thatprecipitated the mitigation is compared to the amplitude of vibrationpredicted by the WellDrill™ model created as discussed above. If thedifference exceeds a predetermined threshold, for example 10%, the modelis revised to provide better agreement. Whether the vibration mitigationwas accomplished by a change in drill mud flow rate, WOB or drill bitRPM is determined in step 602.

If mitigation was accomplished by changing drill bit RPM, steps 604-612are performed. If mitigation was accomplished by decreasing drill bitRPM, then revisions to the model are made as specified in steps 606-608to determine whether any result in a revised prediction of vibrationthat does not deviate from the measured value by more than the thresholdamount. Thus, the, model is first revised by increasing the size of thebore hole used in the model by a predetermined amount. Although notindicated in the flow chart, if an increase in the borehole size by thepredetermined about results in a reduction in the deviation between themeasured and predicted vibration but does not reduce the deviation belowthe threshold, repeated incremental increases in bore hold size areattempted until the deviation drops below the threshold or the totalincrease in borehole size used in the model reaches a predeterminedlimit. If increases in borehole size up to the predetermined limit donot result in a reduction in the deviation below the threshold, then thesoftware moves on to the next parameter in the hierarchy, in this case,the size of the drill bit used in the model. As indicated in step 606,the size of the drill bit used in the model is reduced in a mannersimilar to that discussed above in connection with the increase in holesize, if that does not result in agreement then, in succession, adecrease in the damping coefficient, a decrease in the drill stringstiffness (i.e., the modulus of elasticity), and an increase instabilizer size are attempted in a similar manner. If a change in one ofthese parameters reduces the deviation between measured and predictedvibration below the threshold, the model is revised in step 622 and therevised model used thereafter. If none of these successfully reduce thedeviation between measured and predicted vibration, then, although notindicated in the flow chart, the model would be revised in step 622 toincorporate the value of the parameter that effected the biggestreduction in the deviation. As similar approach is followed inconnection with the other attempts to revise the model that areillustrated in FIG. 13, discussed below.

Similar to the procedure discussed above, if mitigation was accomplishedby increasing drill bit RPM, then revisions to the model are made asspecified in steps 610-612 to determine whether any result in a revisedprediction of vibration that does not deviate from the measured value bymore than the threshold amount. Thus, the model is first revised bydecreasing the size of the bore hole, followed by, in succession,increasing the damping coefficient, and increasing the stiffness of thedrill string to determine whether any of these revisions reduce thedeviation between the measured and predicted vibration below thethreshold amount.

Similar to the procedure discussed above, if mitigation was accomplishedby changing WOB, then revisions to the model are made as specified insteps 614-616 to determine whether any result in a revised prediction ofvibration that does not deviate from the measured value by more than thethreshold amount. Thus, the model is first revised by increasing WOB,followed by, in succession, decreasing WOB, increasing drill stringstiffness and decreasing drill string stiffness to determine whether anyof these revisions reduce the deviation between the measured andpredicted vibration below the threshold amount.

Similarly to the procedure discussed above, if mitigation wasaccomplished by changing drilling mud flow rate, then revisions to themodel are made as specified in steps 618-620 to determine whether anyresult in a revised prediction of vibration that does not deviate fromthe measured value by more than the threshold amount. Thus, the model isfirst revised by increasing mud motor RPM, followed by, in succession,decreasing mud motor RPM, increasing drill string stiffness anddecreasing drill string stiffness to determine whether any of theserevisions reduce the deviation between the measured and predictedvibration below the threshold amount.

Preferably, when using the methodology discussed above, the model isrevised only if the changed parameter causes the deviation in thevibration at issue (e.g., the axial vibration at a particularaccelerometer location) to drop below the threshold amount, withoutcausing the deviation in another vibration (e.g., another mode ofvibration or vibration in the same mode at another location) to exceedthe threshold amount.

The methodology discussed above, in which the successful mitigation oflost performance due to high vibration is used to guide the revision ofthe model to reduce deviations between measured and predicted vibration,cannot be employed if the attempted mitigation was unsuccessful or ifmitigation was unnecessary. Accordingly, an alternative method isemployed under such circumstances, as shown in FIG. 14. In thealternative method, the hierarchy in parameters for which changes areattempted is preferably mud motor RPM, followed by WOB, followed byborehole size.

It is determined in step 700 whether the deviation between the measuredand predicted vibration exceeds the predetermined threshold amount. Ifso, in steps 702-712, incremental increases and decreases in the mudmotor RPM used in the model, within a prescribed permissible range ofvariation, are attempted until the deviation drops below the thresholdamount. If no value of the mud motor RPM within the permissible range ofvariation results in the deviation in the vibration at issue droppingbelow the threshold amount, the software revises the mud motor RPM usedin the model to the value that reduced the deviation the most, but thatdid not cause the deviation between the predicted and measured valuesfor another vibration to exceed the threshold amount.

If variation in mud motor RPM does not reduce the deviation below thethreshold amount, in steps 714-724 the WOB used in the model is thendecreased and increased, within a prescribed permissible range ofvariation, until the deviation drops below the threshold amount. If novalue of WOB within the permissible range of variation results in thedeviation between the measured and predicted vibration dropping belowthe threshold amount, the software revises the WOB used in the model tothe value that reduced the deviation the most, but that did not causethe deviation between the predicted and measured values for anothervibration to exceed the threshold amount.

If variation in WOB does not reduce the deviation below the thresholdamount, in steps 726-736 the assumed borehole size used in the model isthen decreased and increased within a prescribed permissible range ofvariation—which range may take into account whether severe washoutconditions were expected, in which case the diameter could be double thepredicted size—until deviation drops below the threshold amount. If avalue of borehole size results in the deviation dropping below thethreshold amount, without causing the deviation in another vibration toexceed the threshold amount, then the model is revised to reflect thenew borehole size value. If no value of borehole size within thepermissible range of variation results in the deviation between themeasured and predicted vibration dropping below the threshold amount,the software revises the borehole size used in the model to the valuethat reduced the deviation the most, but that did not cause thedeviation in another vibration level to exceed the threshold amount.

Alternatively, rather than using the sequential single variable approachdiscussed above, the software could be programmed to performmulti-variable minimization using, for example, a Taguichi method.

If none of the variations in mud motor RPM, WOB and bore hole diameter,separately or in combination, reduces the deviation below the threshold,further investigation would be required to determine whether one or moreof the inputs were invalid, or whether there was a problem down hole,such as a worn bit, junk (such as bit inserts) in the hole, or a chunkedout motor (rubber breaking down).

10. Life Prediction Based On Vibration & Temperature Monitoring

The life of the electronics components is heavily influenced by the timespent at elevated temperatures, as well as the exposure to shock andvibration. The higher the temperature, shock, vibration the greater thelife consumed.

According to the invention, the software 20 calculates the remaininguseful life in components of the bottomhole assembly 6 based on thevibration levels at the location of these components determined by thesoftware during the drilling operation. In particular, the remaininglife in bottomhole assembly components is calculated based on (i) thehistory of measured vibration, (ii) test results of the life thesecomponents at various levels of vibration, and (iii) the temperature towhich the components have been subjected.

According to the Palmgren-Minor theory, cumulative damage due to strainreversals at various amplitudes on fatigue life can be expressed by theequation:

${\frac{n_{1}}{N_{1}} + \frac{n_{2}}{N_{2}} + \ldots + \frac{n_{i}}{N_{i}}} = C$

where:

-   -   n=the number of cycles at which a given stress is applied to the        component.    -   N=is the fatigue life corresponding to that stress.    -   C=a constant determined by experiment.

Therefore, the software uses the following equation, preferably based ontesting at three strain levels—normal, high and severe, to determine theimpact of vibration on fatigue life:

L=(t/T)_(normal)+(t/T)_(high)+(t/T)_(severe)

-   -   Where:    -   t=actual time at each given vibration level—i.e., normal, high        and severe.    -   T=time to failure at each given vibration level based on fatigue        testing the component to failure at each of normal, high and        severe levels of vibration.    -   L=portion of fatigue life used up thus far.

For example, if testing indicated that the life of a component of thebottomhole assembly 6 is 1000 hrs at normal vibration, 100 hrs at a highvibration and 10 hours at severe vibration, and the component has beensubjected to 500 hrs at normal vibration, 10 hrs at high vibration and 1hour at severe vibration, the portion of its life that has been used upis ( 500/1000)+( 10/100)+( 1/10)=0.7.

Since temperature also adversely affects fatigue life, the softwaretakes the measured temperature, sensed by a temperature sensor in theVibration Monitoring Module, into account in predicting life. To accountfor temperature effects, the software uses a revised form of thePalmgren-Minor equation:

L=(t/T)^(m) _(normal)+(t/T)^(m) _(high)+(t/T)^(m) _(severe)

Where m is an experimentally derived factor determined by fitting acurve to a plot of the reduction in fatigue life versus temperature.

Thus, in the example above, if a component has been operating at 125°C., at which temperature it has only 70% of is room temperature life,the tool will have used up all its life after 500 hrs at normalvibration, 10 hrs at high vibration and 1 hour at severe vibration.

Complicating the ability to keep track of the remaining fatigue life isthe fact that after equipment is used to complete a certain task (drilla well), it is then refurbished and sent out to another well. Each wellis unique and imposes different stresses on the components. Therefore,time at temperature, temperature shock and vibration are generallydifferent and each well uses up some of the life of the tool.Consequently, according to the current invention, a memory device thatstores the value of the remaining fatigue life, such as a microchip, canbe incorporated into each critical drill string component, such asdevice 47 incorporated into Vibration Memory Module™ 46 as indicated inFIG. 4. When the component is removed from the well, the software willretrieve the previously stored information on remaining life, update theinformation based on the operation in the current well, and download theupdated information into the memory storage device.

11. Optimizing Drilling Efficiency

In general, the higher the drill bit RPM and the greater the WOB, thehigher the rate of penetration by the drill bit into the formation,resulting in more rapid drilling. However, increasing drill bit RPM andWOB can increase vibration, which can reduce the useful life of the BHAcomponents. In a preferred embodiment, the software automaticallydetermines if the optimum drilling performance is being achieved andmakes recommendations if it is not. According to the invention, thesoftware 20 utilizes the predicted critical speeds at which resonantvibration or stick-slip occurs and the predicted vibration levels, andmeasured rates of penetration, to provide information to the drill rigoperator as to the optimal rate of penetration that can be obtainedwithout incurring excessive vibration. Drilling optimization begins witha pre-run WellDrill analysis. The intent of the analysis is to design aBHA that will drill the planned well, have sufficient strength for theplanned well and to predict critical speeds to avoid. During thepre-analysis process components of the drill string can be moved oraltered to achieve the desired performance. Modifications may includeadding, subtracting or moving stabilizers, selecting bits based onvibration excitation and performance and specifying mud motors powersections, bend position and bend angle. Based on the analysis theinitial conditions are set.

Once drilling begins optimization trials can take place. Normally theonly variable that the drill rig operator can change are drill stringRPM, WOB and mud flow rate (which affects the drill bit RPM). The trialsinvolve altering the drilling variable to determine their effect ondrilling efficiency. Typical the driller or an automated system wouldvary the drilling variables by −20%, −10%, 0%, +10% and +20%. Thesetests can be run without greatly affecting the drilling operation.Another method is drilling run off tests. These tests are performed byweighting up the bit to it upper limit, locking the draw works so thatthe drill string is fixed at the surface. Then, as the well is drilled,the compression in the pipe is relieved and reduces the WOB, allowingthe measurement of the ROP at a constant drill string RPM but varyingWOB. This process is repeated at several drill string RPMs and mud flowrates. The results are then ranked as to their drilling performance.

Using the drilling performance results and predicted vibration levels,the software recommends the best set of variables that optimize ROPwithout producing excessive vibration. Alternatively, the software willgenerate graphs showing both the predicted axial vibration versus WOBand the measured rate of penetration versus WOB. Using these two graphs,the operator can select the WOB that will result in the maximum rate ofpenetration without incurring excessive axial vibration. Similar graphswould be generated for other modes of vibration.

In any event, whether the software recommended the optimum operatingparameters or the drill rig operator selected them from informationprovided by the software, the operator would continue to drill at theseconditions until there was a change to the drilling conditions. Changesmay include bit wear, different formation type, changes in inclination,azimuth, depth, vibration increase, etc. At this time, the optimizationprocess should be re-run.

One method of optimizing drilling efficiency is shown in FIG. 15. Instep 900, drilling tests are performed, as discussed above, so as toobtain a data base of ROP versus WOB and drill string and drill bit RPM.In step 902, the software determines the critical speeds of the drillstring and then determines whether operation at the WOB and drillstring/drill bit RPMs that yielded the highest ROP based on the drillingtest data will result in operation at a critical speed. Alternatively,the software can predict the level of vibration at the criticalcomponents in the drill string at the WOB and drill string/drill bitRPMs that yielded the highest ROP to determine whether operation at suchconditions will result in excessive vibration of the criticalcomponents. In any event, if the software predicts vibration problems atthe operating conditions that resulted in the highest ROP, it will thencheck for high vibration at the other operating conditions for whichdata was obtained in the drilling tests until it determines theoperating conditions that will result in the highest ROP withoutencountering high vibration. The software will then recommend to theoperator that the drill string be operated at the WOB anddrillstring/drill bit RPMs that are expected to yield the highest ROPwithout encountering excessive vibration.

While operating at the parameters recommended by the software in step904, data will be periodically obtained from the downhole and surfacesensors, as discussed above, in step 906. As also discussed above, instep 908, the software will determine whether the measured and predictedvibration agree and if they do not, the model will be revised in step910. Thus, the optimization of drilling parameters will always beperformed using an updated WellDrill model that predicts vibration basedon real-time data from the sensors. In step 912, the software determineswhether, based on the sensor data, the vibration in the drill string ishigh, for example, by determining whether the drill string operation isapproaching a new critical speed or whether the vibration at a criticalcomponent exceeds the maximum for such component. If the vibration ishigh, then step 902 is repeated and the software determines another setof operating parameters that will result in the highest expected ROPwithout encountering excessive vibration. Based on data from the ROPsensor 34, in step 914, the software determines whether the ROP hasdeviated from that expected based on the drilling test. If it has, thesoftware may recommend that further drilling tests be performed tocreate a new data based of ROP versus WOB and drill string/drill bitRPM.

As an example, suppose that a drilling test produced the following ROPdata (for simplicity, assume no mud motor so that the drill bit RPM isthe same as the drill string RPM):

TABLE XI WOB, lbs 200 RPM 300 RPM 10k 10 fpm 20 fpm 20k 15 fpm 25 fpm30k 20 fpm 30 fpm 40k 25 fpm 33 fpm

Using the WellDrill model, the software will predict whether operationat 40 k WOB and 300 RPM (the highest ROP point in the test data) willresult in operation at a critical speed or in excessive vibration at acritical component. If it does not, the software will advise theoperator to operate at 40 k WOB and 300 RPM. Thereafter, each time a newset of sensor data was obtained (or a new section of drill pipe added)the software will (i) revise the model if the predicted vibration at theaccelerometer locations does not agree with the measured vibration and(ii) determine whether the vibration is excessive, for example, by usingthe revised model to determine the vibration at the critical componentsby extrapolating the measured vibration, as previously discussed.

If at some point, it is determined that the vibration of the drillstring has become excessive, the software will predict the vibration at30 k WOB and 300 RPM (the second highest ROP point from the drillingtest data) and recommend that the operator go to those operatingconditions unless it predicted excessive vibration those conditions.Thereafter, each time another set of sensor data was obtained (and themodel potentially revised), the software will predict whether it wassafe to again return to the initial operating conditions associated withthe highest ROP (40 k WOB/300 RPM) without encountering excessivevibration. If the software never predicts that it is safe to go back tothe initial operating conditions but, at some point, it determines thatthe vibration has again become excessive, it will predict vibration atthe two sets of parameters that resulted in the third highest ROP—20 kWOB/300 RPM and 40 k WOB/200 RPM—and recommend whichever one resulted inthe lower predicted vibration.

In some embodiments, instead of merely recommending changes that theoperator makes to the operating parameters, the method described abovecould be implemented by the software automatically changing theoperating parameters so as to automatically operate at the conditionsthat resulted in maximum drilling performance.

Rather than using ROP as the basis for optimization, the software canuse the Mechanical Specific Energy (“MSE”) to predict the effectivenessof the drilling, rather than the ROP. The MSE can be calculated, forexample, as described in F. Dupriest & W. Koederitz, “Maximizing DrillRates With Real-Time Surveillance of Mechanical Specific Energy,”SPE/IADC Drilling Conference, SPE/IADC 92194 (2005) and W. Koederitz &J. Weis, “A Real-Time Implementation Of MSE,” American Association ofDrilling Engineers, AADE-05-NTCE-66 (2005), each of which is herebyincorporated by reference in its entirety. Specifically, the MSE iscalculated for each combination of RPM and WOB that does not result inexcessive vibration from the equation:

MSE=[(480×T×RPM)/(D ²×ROP)]+[(4×WOB)/(D ²×π)]

Where:

-   -   MSE=Mechanical Specific Energy    -   T=drill string torque, ft-lb    -   RPM=rotational speed of the drill bit    -   ROP=rate of penetration, ft/hr    -   WOB=weight on bit, lb    -   D=diameter of drill bit, inches

For purposes of calculating MSE, the software obtains the value of ROPfrom drilling tests, as described above, as well as the torques measuredduring the drilling tests. Based on these calculations, the softwarewould recommend to the operator that the drill bit RPM and WOB berevised to the pair of values that yielded the highest MSE value.

12. Determining Operating Efficiency of Mud Motor

Sometimes the cause of lost drilling performance is due to conditionsthe driller cannot change but he should be made aware of them so he canplan corrective action. In particular the mud motor wear due to theerosive and abrasive conditions with the flow of drilling mud throughthe motor. This causes wear on both the rotor and stator and similarconditions occur in other tools such as a turbodrills. There is adefinite known relationship between flow into the motor and output speedand torque. As the motor wears the speed drops for a given torque. Thisloss in power is due to leakage thru the motor seals and the leakageincreases with increasing load or torque on the motor. Load can bemeasured by the pressure drop across the motor. Speed can be measureddirectly by the drill bit speed or frequency or by the notation speed ofthe mud motor by performing an Fast Fourier Analysis of the downholevibration or the surface vibration. A loss in speed for a given flow anddifferential pressure represents a loss in efficiency of the motor. Bycomparing the efficiency of a new motor to the actual efficiency we canalert the driller to a drilling performance loss.

Although the invention has been described with reference to specificmethodologies for monitoring vibration in a drill string, the inventionis applicable to the monitoring of vibration using other methodologiesbased on the teachings herein. For example, although the invention hasbeen illustrated using mud motor rotary drilling it can also be appliedto pure rotary drilling, steerable systems, rotary steerable systems,high pressure jet drilling, and self propelled drilling systems, as wellas drills driven by electric motors and air motors. Accordingly, thepresent invention may be embodied in other specific forms withoutdeparting from the spirit or essential attributes thereof and,accordingly, reference should be made to the appended claims, ratherthan to the foregoing specification, as indicating the scope of theinvention.

1. A method of monitoring the operation of a drill string drilling intoan earthen formation so as to form a bore hole using a drill bit,comprising the steps of: (a) drilling a bore hole having a firstdiameter in said earthen formation by rotating said drill bit at a firstrotary speed and applying a first weight on said bit; (b) making adetermination of the value of said first rotary speed at which saiddrill bit rotates; (c) making a determination of the value of said firstweight on said bit; (d) making a determination of the value of saidfirst diameter of said bore hole; (d) measuring vibration in said drillstring at least one predetermined location along said drill string whilerotating said drill bit at said first speed and applying said firstweight on said bit; (e) using a finite element model of said drillstring to predict the vibration in said drill string at said at leastone predetermined location based on said determined values of said firstrotary speed of said drill bit, said first weight on bit and said firstbore hole diameter; (f) comparing said measured vibration to saidpredicted vibration and determining the difference therebetween; (g)revising said finite element model so as to reduce said differencebetween said measured vibration and said vibration predicted by saidmodel; (h) drilling a bore hole having a second diameter in said earthenformation by rotating said drill bit at a second rotary speed andapplying a second weight on said bit; (i) making a determination of thevalue of said second rotary speed at which said drill bit rotates; (j)making a determination of the value of said second weight on said bit;(k) making a determination of the value of said second diameter of saidbore hole; (l) using said revised finite element model of said drillstring to predict the vibration in said drill string based on saiddetermined values of said second rotary speed of said drill bit, saidsecond weight on bit and said second bore hole diameter.
 2. The methodaccording to claim 1, wherein said finite element model of said drillstring predicts vibration based on a set of operating parameters, saidset of operating parameters comprising rotary speed of said drill bit,weight on said bit, and diameter of said drill bit, and wherein the stepof revising said finite element model so as to reduce said differencebetween said measured and predicted vibration comprises adjusting thevalue of a plurality of operating parameter in said set of operatingparameters so as to identify an adjustment that reduces said differencebetween said predicted and measured vibration below a predeterminedthreshold.
 3. The method according to claim 2, wherein said plurality ofoperating parameters are adjusted one at a time so as to identify anadjustment that reduces said difference between said predicted andmeasured vibration below said predetermined threshold.
 4. The methodaccording to claim 2, wherein said plurality of operating parameters areadjusted by adjusting two or more parameters at a time so as to identifyan adjustment that reduces said difference between said predicted andmeasured vibration below said predetermined threshold.
 5. The methodaccording to claim 1, wherein said first and second bore hole diametersare approximately equal.
 6. A method of monitoring the operation of adrill string drilling into an earthen formation so as to form a borehole using a drill bit located in a bottom hole assembly, comprising thesteps of: a) determining the values of a plurality of operatingparameters associated with said underground drilling operation by takingmeasurements from a plurality of sensors, at least a portion of saidsensors located in said bottom hole assembly; b) determining from saiddetermined values of said operating parameters whether each of aplurality of predetermined symptoms of lost drilling performance arepresent in said drilling operation; c) identifying the probability thateach of said parameters determined to be present in said drillingoperation are caused by each of a plurality of predetermined causes oflost drilling performance; d) combining said identified probabilitiesfor each of said predetermined causes of lost drilling performance so asto determine the most likely cause of lost drilling performance presentin said drilling operation.
 7. The method according to claim 6, furthercomprising the step of: e) adjusting at least one operating parameterassociated with said drilling operation based on said cause of lostdrilling performance determined to be most likely present in saiddrilling operation.
 8. The method according to claim 6, wherein saidplurality of operating parameters comprises the vibration of said drillstring.
 9. The method according to claim 6, wherein said plurality ofoperating parameters comprises the amplitude of vibration of said drillstring in the axial and lateral and torsional vibratory modes.
 10. Themethod according to claim 6, wherein said plurality of operatingparameters comprises the frequency of the vibration of said drillstring.
 11. The method according to claim 6, wherein said plurality ofoperating parameters comprises the weight on said drill bit and therotary speed of said drill bit.
 12. The method according to claim 6,wherein the plurality of predetermined symptoms of lost drillingperformance comprises vibration of said drill string.
 13. The methodaccording to claim 6, wherein the plurality of predetermined symptoms oflost drilling performance comprises stick-slip.
 14. The method accordingto claim 6, wherein the step of combining said identified probabilitiesfor each of said predetermined causes of lost drilling performancecomprises summing said identified probabilities.
 15. The methodaccording to claim 6, wherein the step of identifying the probabilitythat each of said parameters determined to be present in said drillingoperation are caused by each of a plurality of predetermined causes oflost drilling performance comprising retrieving said probabilities froma data base in which said probabilities are stored.
 16. A non-transitorycomputer-readable storage medium having stored thereoncomputer-executable instructions for performing a method of monitoringthe operation of a drill string drilling into an earthen formation so asto form a bore hole using a drill bit, the method comprising the stepsof: a) determining the values of a plurality of operating parametersassociated with said underground drilling operation by takingmeasurements from a plurality of sensors, at least a portion of saidsensors located in said bottom hole assembly; b) determining from saiddetermined values of said operating parameters whether each of aplurality of predetermined symptoms of lost drilling performance arepresent in said drilling operation; c) identifying the probability thateach of said parameters determined to be present in said drillingoperation are caused by each of a plurality of predetermined causes oflost drilling performance; d) combining said identified probabilitiesfor each of said predetermined causes of lost drilling performance so asto determine the most likely cause of lost drilling performance presentin said drilling operation.
 17. The computer-readable storage mediumaccording to claim 16, wherein the step of identifying the probabilitythat each of said parameters determined to be present in said drillingoperation are caused by each of a plurality of predetermined causes oflost drilling performance comprising retrieving said probabilities froma data base in which said probabilities are stored.
 18. A method ofmonitoring the operation of a drill string drilling into an earthenformation so as to form a bore hole using a drill bit, comprising thesteps of: a) operating said drill string at a first set of operatingparameters, said first set of operating parameters comprising the speedat which said drill bit rotates; b) determining the values of saidparameters in said first set of operating parameters; c) inputting saiddetermined values of said parameters in said first set of operatingparameters into a finite element model of said drill string; d) usingsaid finite element model of said drill string with said inputted valuesof said parameters to determine at least a portion of the vibratory modeshape of said drill string when operating at said first set of operatingparameters; e) using said portion of said vibratory mode shape todetermine the relationship between the amplitude of vibration at saidfirst location to the amplitude of vibration at a second location whenoperating at said first set of operating parameters; f) measuring theamplitude of vibration of said drill string at said second location whenoperating at said first set of operating parameters; g) determining theamplitude of vibration of said drill string at said first location byapplying to said measured vibration at said second location saidrelationship between the amplitude of vibration at said first locationto said amplitude of vibration at a second location determined from saidportion of said vibratory mode shape.
 19. The method according to claim18, wherein using said portion of said vibratory mode shape to determinethe relationship between the amplitude of vibration at said firstlocation to the amplitude of vibration at a second location comprisesdetermining the ratio of said amplitude of vibration at said firstlocation to said amplitude of vibration at said second location.
 20. Themethod according to claim 19, wherein the step of applying to saidmeasured vibration at said second location said relationship comprisesmultiplying said amplitude of vibration measured at said second locationby said ratio.
 21. A non-transitory computer-readable storage mediumhaving stored thereon computer-exectuable instructions for a method ofmonitoring the operation of a drill string drilling into an earthenformation so as to form a bore hole using a drill bit, the methodcomprising the steps of: a) determining the values of the parameters ina first set of operating parameters at which said drill string isoperating; b) inputting said determined values of said parameters insaid first set of operating parameters into a finite element model ofsaid drill string; c) using said finite element model of said drillstring with said inputted values of said parameters to determine atleast a portion of the vibratory mode shape of said drill string whenoperating at said first set of operating parameters; d) using saidportion of said vibratory mode shape to determine the relationshipbetween the amplitude of vibration at said first location to theamplitude of vibration at a second location when operating at said firstset of operating parameters; e) measuring the amplitude of vibration ofsaid drill string at said second location when operating at said firstset of operating parameters; f) determining the amplitude of vibrationof said drill string at said first location by applying to said measuredvibration at said second location said relationship between theamplitude of vibration at said first location to said amplitude ofvibration at a second location determined from said portion of saidvibratory mode shape.
 22. A method of monitoring the operation of adrill string drilling into an earthen formation so as to form a borehole using a drill bit, comprising the steps of: a) applying a torque tosaid drill string at a location proximate the surface of the earth so asto rotate said drill string, said drill string undergoing angulardeflection between said drill bit and said location at which said torqueis applied; b) determining the values of parameters in a first set ofoperating parameters associated with said rotation of said drill string;c) inputting said determined values of said parameters in said first setof operating parameters into a finite element model of said drillstring; d) using said finite element model of said drill string withsaid inputted values of said parameters to determine the angulardeflection in said drill string at at least first and second locationsalong the length of said drill string when operating at said first setof operating parameters; e) using said angular deflections at said firstand second locations along said drill string to determine therelationship between the torque on said drill string at said first andsecond locations; f) measuring the torque on said drill string at saidsecond location when operating at said first set of operatingparameters; g) determining the torque on said drill string at said firstlocation by applying to said measured torque at said second locationsaid relationship between the torque on said drill string at said firstlocation to the torque on said drill string at the second location. 23.A method of monitoring the operation of a drill string having a drillbit drilling into an earthen formation, comprising the steps of: a)rotating said drill bit at a first rotary speed so that said drill bitforms a bore hole in said earthen formation, said drill string vibratingin a lateral vibration mode; b) generating a signal representative ofsaid vibration of said drill string in said lateral vibration mode assaid drill bit drills into said earthen formation; c) analyzing saidsignal so as to determine the backward whirl frequency of said vibrationof said drill string in said lateral vibration mode; d) determining thediameter of said bore hole being drilled by said drill bit from saidbackward whirl frequency.
 24. The method according to claim 23, whereinthe step of analyzing said signal comprises performing a Fourieranalysis of said signal.
 25. The method according to claim 23, whereinthe step of determining the diameter of said bore hole comprisescalculating d×(1+w/BWF), wherein d is the diameter of said drill bit, wis the rotary speed of said drill bit, and BWF is said backward whirlfrequency.
 26. A method of monitoring the operation of a drill stringhaving a drill bit drilling into an earthen formation, comprising thesteps of: a) determining a set of operating parameters for said drillstring that will result in the maximum rate of penetration of said drillbit into said earthen formation; b) inputting said set of operatingparameters into a finite element model of said drill string; and c)using said finite element model with said inputted set of operatingparameters to predict the vibration in said drill string that willresult from operation of said drill string according to said set ofoperating parameters.
 27. The method according to claim 26, wherein thestep of determining said set of operating parameters that will result inthe maximum rate of penetration comprises the step of operating saiddrill string at a plurality of sets of operating parameters andmeasuring the rate of penetration associated with each said set ofoperating parameters.
 28. The method according to claim 26, wherein saidset of operating parameters comprises the rotary speed of said drillstring and the weight applied to said drill bit.
 29. A method ofmonitoring the operation of a drill string having a drill bit drillinginto an earthen formation, comprising the steps of: a) obtaining a database relating sets of operating parameters for said drill string torates of penetration of said drill bit into said earthen formation whenoperating at said sets of operating parameters; b) using a finiteelement model of said drill string and said data base to predict themaximum rate of penetration of said drill string into said earthenformation that will not result in the vibration in said drill stringviolating a predetermined criteria.
 30. The method according to claim29, wherein said predetermined criteria comprises a maximum amplitude ofvibration for at least a portion of said drill string.
 31. The methodaccording to claim 29, wherein said predetermined criteria comprisessaid drill string not operating at a rotary speed that results inresonant vibration of said drill string.